A love-hate relationship is a personal relationship involving simultaneous or alternating emotions of love and enmity. Sometimes the person may love the other person/object, but hate oneself for it. This relationship can, but does not have to, be of a romantic nature. It may occur when people have completely lost the intimacy within a loving relationship, yet still retain some passion for, or perhaps some commitment to, each other.
It is used most frequently in psychology, popular writing and journalism, much more so than in everyday discourse, and almost never amongst the individuals of whom it is predicated. It can be extended to relationships with inanimate objects, or even concepts. In popular journalism, it is often employed speculatively by writers to explain the relationship between celebrity couples who have been divorced, then who reunite (notably Elizabeth Taylor and Richard Burton).
A related theme is "obligatory friendship", where usually one party feels indebted to another and forges a friendship but still holds a grudge over a particular past disappointment or set of disappointments, while the "creditor" in the relationship agrees to the nature of the relationship often for security reasons, but remains aware of the "debtor's" grudge and feels counter-indebted until the cause of the grudge is sufficiently overcome.
It can be argued that, due to the fact that the subjects love each other despite issues they have, a love hate relationship actually represents a stronger bond than a simple love relationship does. Also since a constant hatred is felt, any new issues which emerge are unlikely to put the relationship in jeopardy.
A common feature in (comic) fiction is that the protagonists in a love-hate relationship might term it a hate-hate relationship in moments of especial antagonism.