Steve relays to Brandon that he and Kelly dated and that he broke up with her, while Kelly tells Brenda that Steve is her ex and that he 'doesn't get the message that it's o-v-e-r'. Both are quite agitated with one another; Kelly because Steve spread rumours them, Steve because he's upset that the relationship ended.
Throughout the first season both act somewhat antagonistic, yet fiery toward one another, at times putting their friends Brenda and Brandon in awkward positions. However, over the course of their sophmore and junior year they make peace with each other and become close friends. Although Kelly is shown to care deeply about Steve, she never chooses to start up a relationship with him again, while Steve is seen multiple times wanting to be with Kelly.
It is not specified when the two met; however it is possible they met in high school and dated their freshman year.
After breaking up, Steve spends a lot of time agonising over the break-up in private, while badmouthing Kelly in public. This is somewhat curbed by Brandon's presence in Steve's life, while Kelly is often seen annoyed with Steve, treating him as though he is beneath her. In spite of this conflict, the two actually continuously flirt throughout their sophomore year, and even spend another night together.