In the interest of increasing understanding about this relationship and some of its more complex elements, I thought I'd give a little overview to Dominant/submissive relationships and how it relates to JokerxHarley.

First of all: What is Dominance and submission?

Basically, it refers to a set of behaviours, customs and even rituals relating to the giving and accepting of dominance of a person over another in a relationship. This can happen in an erotic context, or as a lifestyle.

In the most traditional D/s relationships, one partner takes on the position of the 'Dominant' - that is, the authoritative role, whilst the other takes on the 'submissive' - the subordinate role.

There are many different ways that D/s relationships take place. They can include the Dominant controlling the life of the submissive to the extent they direct what the submissive wears and does at all times, with the submissive needing to request permission for every day acts such as going to the bathroom.
Or they can occur on a less pervasive but no less intense or ritualistic scale, such as the power exchange occurring only during sexual activities.
D/s relationships can also include sadomasochistic acts such as torture, humiliation, corporal punishment. But they do not have to.
There is a different between D/s and S&M. The two are often combined for practitioners of these relationships, but not always.

To the uninitiated, a D/s relationship can look merely brutal and cruel and whilst many D/s relationships have representations of brutality and sadomasochistic practises as part of them, in reality D/s relationships are about a consensual power exchange.

Just as the Dominant gets intense gratification and fulfilment from dominating and from providing boundaries within which the submissive must act, so too does the submissive get intense gratification and fulfilment from submitting and performing the Dominant's will.
Without the consent of the submissive and the submissive's active participation, the relationship cannot truly exist.  The submissive is not forced to relinquish their power - they instead willingly hand it over and that is an act of strength and power in itself.
Such relationships also have high levels of trust. The submissive must trust that in the relinquishing of power, the Dominant will take care of them and ensure they are looked after (psychologically and physically) and the Dominant must trust the submissive is genuinely consenting and being forthcoming about their participation and needs.

The power exchange in the relationship is just that - an exchange. Submissives are not unknown for pushing the established boundaries. Because the activity is consensual, submissives may 'act up' in order to receive punishment or simply to push their Dominant into taking things to the next level. Other submissives will take the greatest pleasure in being well-behaved at all times. Some Dominants enjoy a pushy sub, others would rather have an obedient one. Like most things in life, there are endless variations.

Again to the uninitiated, such relationships often look as though the Dominant is the one getting the most out of it. On the contrary, the Dominant is invested in meeting the expectations of their submissive as well.  The fact is, both parties involved in the relationship are there because this type of relationship is satisfying to them. They are generally informed and aware and actively involved.

D/s and JokerxHarley

Joker and Harley have a very clear D/s relationship, but it is one that is, like themselves, much larger than life and very unhealthy.
Because of the nature of D/s relationships it can happen that unstable participants can lose sight of the lines between consensuality and abuse, which leads to a D/s relationship which is also abusive. Joker and Harley clearly have one of these.

It is also unlikely that, although both parties are 'aware' on some level of the D/s dynamic between them, this relationship has been negotiated, reasonable boundaries have been set, or it has been formally acknowledged in any way. Indeed, just the opposite.
In the D/s scene, this usually happens - agreed upon activities will be discussed, contracts will be written and ceremonies of commitment are undertaken. There is a general adherence to the credo of 'safe, sane and consensual' and I don't think anyone will argue this is noticeably absent from Joker and Harley's relationship.
What we see is a 24/7 (lifestyle) D/s relationship without boundaries, limits or sanity. It is not play, and it doesn't ever stop. It's all the way and simply a part of life for both of them. It's dangerous, all-consuming and there isn't any safe-word. It's a very exciting idea to the hardcore D/ser, but is not practical in reality and, generally speaking, impossible to do healthily.

Nonetheless, despite this, both Joker and Harley get clear gratification from this relationship.
Joker, as a narcissistic egomaniac with a naturally forceful and dominating personality, would find his needs met in Harley's adoration and devotion. His sadistic streak can be gratified with her and he can enjoy the power he wields over her in her inability to ever truly give him up.
Harley, meanwhile, can gratify her need to adore and nurture someone who loves the attention (most of the time).  She can also satisfy her lust for thrillseeking with a man who has no limits and will continue to push hers. Her masochism can be indulged with his violence.

The relationship's intensity is such that they're always on an emotional rollercoaster together. This can be as addictive as any drug and is no doubt a key element in the cyclical nature of their relationship. Splitting up - breaking the D/s ties - only to reunite and re-establish them would be intoxicating for people involved in this sort of dynamic.

Joker provides Harley with a sense of purpose and self-worth, something she was shown to have been seeking when she encountered him. Through this relationship and following a life of crime, Harley has secured a great deal of attention on a high profile scale. He also provides her with a structure of reward and punishment, as perverse as it may be, that she clearly needs and desires.

D/s relationships, although there may be a high level of physicality, primarily take place on a psychological level. It is easy enough to hit someone or allow yourself to be hit. The act of Dominating, or submitting, on the other hand is quite different. It takes place on a different psychological level that allows whatever activity is being carried out to be more intense and more exciting.
Sometimes no physical interaction is required; simply knowing that one is submitting to one's Dominant, or one has control over one's submissive, is enough to create an intoxicating and delicious state of being.

Psychology plays an enormous part in Joker and Harley's relationship and is definitely where the abusiveness is most on show. Joker delights in manipulating and tormenting Harley on an emotional level - teasing and denying her - and possessing her soul in madness. He was actually responsible for breaking her mind and binding her to him in obsession. On some level Harley is aware of this and delights in it. She loves that she has transgressed the reasonable boundaries of society and while she occasionally makes attempts at rehabilitation, ultimately she can never commit to it. On the other hand, her committal to Joker is absolute. As someone who demonstrated absolute determination to what she has wanted - her scholarship, her degree and her man - it's interesting that she can't - or won't - stick to sanity.
It is clear also that Harley gets immense joy and satisfaction from being by Joker's side and seeing his needs are met, just as he gets enjoyment from involving her in key roles in his schemes and sharing a joke with her on a level he doesn't with anyone else, except Batman. (Although Batsy rarely sees the joke.)

Power exchange is very much an active element of this relationship and further reflects the consensuality. Harley is happy to be submissive, to even be cowed and intimidated, so long as Joker is playing within whatever boundaries they implicitly understand. When he transgresses these, she retaliates and he has to comply in order for her to back off. Also, Joker definitely bit off a little more than he could chew with Harley. Her devotion and neediness is such that it often frustrates him, or outright freaks him out, which must be a shock to someone as conceited as he is.
There is also some indication that Harley, who definitely plays dumber than she is, may subtly manipulate Joker with deliberate 'goof-ups', or calculated 'disingenuous' behaviour in order to secure his attention.
She definitely controls his environment through taking the pressure of him to see to basic, everyday needs. He is so frenetically insane that these things prove distractions to him and Harley builds up a more or less orderly structure around him. If she's not around, this quickly collapses leading to his frustration and discomfort.
Although he has the official power in this relationship, it is at least partially due to the fact she permits him to.

D/s and Sex

Due to the fact that the relationship operates within a D/s framework, it would extend to sexual interaction as well. People rightly argue that Joker is not someone who has ever appeared overly-interested in traditional forms of sex - but Joker nonetheless seems to be a very sexual, sensual being. Often in D/s relationships, traditional sex is enjoyed but is not the only way the participants obtain sexual gratification. The activity of a submissive carefully polishing their Dominant's shoe, for example, can be as fully gratifying sexually as sex itself would be to another couple.
Given the two clowns' insanity and perverse sense of humour as well as the love Joker has of pushing limits, it's easy to imagine them having sexual interaction on multiple other levels. 'Sexual interaction' does not necessarily mean genital, or even physical, contact. It can involve rituals such as dressing one partner, performing an activity as instructed, meting out a punishment - or even, in Joker and Harley's case, committing a crime, a murder or act of destruction.

Daddy/girl and JokerxHarley

Another level this relationship works on, a subset of D/s relationships, is the Daddy/girl dynamic.
Daddy/girl is very similar to a general D/s relationship in that one participant - the Daddy - acts as the authority and the other - the girl - acts as the subordinate.
This relationship dynamic generally involves a fetishising or eroticising of parent/child roles but does not always have anything to do with an active incest fantasy. This relationship dynamic also is referred to as 'ageplay' as although there might not be much - or any -difference in the participants' ages, a crucial element of the relationship is the 'girl' acting much younger.
These relationships can differ from more straightforward D/s relationships in that while there is discipline, authority, submission, reward and punishment, there is also a lot of nurturing and care taking.
When 'in role' as the 'girl', the submissive often experiences a sense of freedom from adult concerns, allowing a great deal of relaxation to take place. In this role, the submissive can be free to be immature and childish, unrestrained and uninhibited, knowing the Daddy is there to provide direction, structure and discipline.
I feel you can actively see this taking place between Joker and Harley although it becomes as twisted as they are.  Joker initiates Harley into his world and educates her in the way of crime, madness and mayhem. He can be very coddling and indulgent of her, treating her like a little girl. For Harley's part, she is extremely immature in many ways and definitely left behind responsibility when she entered Joker's world. His insanity allows her to be completely free and yet his domineering nature assures that she still has expected boundaries to work within.
Joker did create Harley and so, in a way, he is her father. The relationship is not literal, but symbolic, and can prove highly exciting and stimulating to those involved in it.
Again, psychology plays a large part here. Harley was ambitious and self-assured before Joker twisted her mind. Now she is a playful girl-woman. That would definitely tickle Joker's perverse fancy, to know he was the cause of such regression. Meanwhile, Harley gets the enjoyment of knowing she gave it all up for her man, and of providing entertainment to him.

Consensual Abuse

I feel I need to stress again that, whilst these relationships are usually enacted in a healthy way, this is obviously not the case with Joker and Harley. Given their insanity, neither would be good (and in Joker's case, concerned with) setting appropriate boundaries or knowing when to stop. Joker ends up being abusive to Harley on two levels - one, with his inability to relate adequately to other humans and so simply acting without regard for others - and two, with his keen astuteness of human psychology, doing it with deliberate intent because it amuses him. Harley, while she plays the game back, is unable to determine clear limits for herself.

In this way the abuse becomes an accepted and integrated part of the relationship. To expect Joker to behave in any other way is impossible and Harley is quite aware of who and what he is. I'm not saying that's right, or ideal - but it is a choice she actively makes throughout the course of the relationship. To claim that Harley is naive and ignorant of this is to ignore all of her very canny and astute behaviour at other times.

And yet, as we have seen in many of their stories, the relationship as it is, is also something they are both happy with. For more detail on the specifics of this, please read the Relationship Evolution article, which deals with stories such as 'My Boyfriend's Back', 'Beware the Creeper', 'Harlequinade', 'The Bride of the Joker', '24 Hours' and others. They are both invested in it - no matter how much Joker complains or Harley swears him off - and are gratified by it. They show each other affection and also a great deal of trust.

Trust is critical in any of these relationships, even in one that isn't defined or limited. And that's not to say trust isn't misplaced in this relationship - due to those absent limits, it definitely is! And yet there is trust. This is not the sort of every-day trust in which you believe what the other partner says at all times. It's trust that the other partner understands what each participant's particular stake is and that that will be fulfilled - even if, as in this relationship - that doesn't take place in the most healthy or respectful way.

The point is, as unhealthy as this is, it is something both participants are happy to be involved in. It may not be ideal to the onlooker, but it suits the two of them and fulfils needs they both have that are complemented by the precise personality and nature of the other. This is made absolutely clear, just as the unhealthy and messed-up elements are too. While relationships like this may seem distasteful to those who aren't into these particular dynamics, that doesn't mean they're not fulfilling and enjoyable for those who are involved in them.

It's Never Just You

From a very young age my natural inclination was towards D/s relationships and it is something I instinctively recognised in the JokerxHarley relationship, although at the time I was not aware of the kink scene and certainly did not have the language to express what it was I perceived. Returning to the fandom with more maturity and several years of experience in the kink scene, I can now fully comprehend the complexity of this relationship.

To my delight, I quickly discovered I was far from the only one and that many other fans of this pairing also recognise the consensual D/s Daddy/girl nature of this relationship.

We perceive the twistedness of it, but we also perceive the genuine affection and mutual gratification. It appeals to us. It's bent, twisted, sick and wrong - and maybe we are too.

But we kinda enjoy that. :)

READING:
Dominance/submission
Daddy/girl