A love-hate relationship is a personal relationship involving simultaneous or alternating emotions of love and enmity. This relationship does not have to be of a romantic nature, and may be instead of a sibling one. 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.
The term is used most frequently in psychology, popular writing and journalism. It can be applied to relationships with inanimate objects, or even concepts. It is sometimes employed by writers to refer to relationships between celebrity couples who have been divorced, then who reunite (notably Elizabeth Taylor and Richard Burton or Eminem and Kimberly "Kim" Scott).
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.
The concept is frequently used in teen romance novels where two characters are shown to hate each other but show some sort of affection or attraction towards each other at certain points of the story. The concept of a love-hate relationship is frequently used in teen novels to describe the romance between a good girl and a bad boy.