Wuthering Heights has evoked many reactions from many people in the centuries since it was written, from disgust to fascination. Multiple possible readings exist, and every one of its characters, each deeply flawed, has received considerable attention. Heathcliff and Catherine remain at the center of the majority of analyses, however. What one makes of Heathcliff—whether he is a villain, victim, or misunderstood Byronic hero—heavily influences what one makes of the novel and of the relationship he shares with Catherine.
One of the favored interpretations, at least in popular culture, holds that Heathcliff is a Byronic hero and paints Heathcliff and Catherine as star-crossed lovers playing out a timelessly tragic love story. This view, however, is influenced by more than just the text—many more people have seen film versions of Wuthering Heights than have read the novel, and these film versions are all too often at best incomplete, and at worst wholesale rewrites of Emily Bronte's story. Early reviews and analyses of the novel tended not to take this view, implying that it is a more recent development influenced by materials outside the text.
Wuthering Heights is one of my favorite pieces of classic literature and I think reducing it to a romance does a great disservice to Emily Bronte's powers as both an observer and as a writer. As a romance the novel is merely crude and unpleasant. As a Gothic deconstruction of romances and Romantic literature, however, it becomes a brutal evisceration of common Romantic ideals and tropes.
If you need a refresher on the characters and plot of Wuthering Heights, you might begin on the story page. Otherwise feel free to begin exploring early reviews of the novel and the various film versions, or skip straight to the analysis—which touches but does not strictly rely on the historical and cultural context that the films and reviews represent.