Drusilla (Juliet Landau) first turned up in Sunnydale with Spike during the second season of Buffy the Vampire Slayer. At some point before her arrival in Sunnydale Drusilla had been attacked and severely injured by an angry mob in Prague, leaving her in a weakened and frail condition. Spike brought her to the Hellmouth in the hope that its energy would help to restore Drusilla’s strength and health.
Drusilla was quite mad – even by vampiric standards. She also had vivid visions that contained possible glimpses of the future, especially involving traumatic events, and could also see into people’s minds and project false imagery into them
But it soon became clear that Spike and Drusilla shared a history with both Angel and Darla; their backstory history unfolded in flashbacks scattered among numerous episodes of both Buffy and Angel. It was eventually revealed that Darla was the vampire who ‘made’ Angel, who in turn ‘made’ Drusilla; so when Drusilla remade Darla in ‘The Trial’, Darla became both Drusilla’s vampiric grandmother and her daughter – no wonder they’re a strange pair.
Like Darla, Drusilla survived her encounters with the Slayer to become of the very few recurring vampire characters in Buffy, and then made the transition to being a recurring character in Angel.