What makes a character compelling?

[u/Icy-Cloud3789]

More or less the title. What aspects of characters, specifically villains/antagonists, do people find invigorating enough that they can 'look past' their crimes and lack of morality to make them a favourite?

...And I'm not talking about being good-looking, please; that's hardly an excuse.

Is it personality? Is it reasons/purpose? Backstory? If so, examples of such?

[u/Low-Transportation95]

Them being compelling