While trying to track down her mother, Claire Novak (Kathryn Love Newton) ends up in hospital and the police contact her father, Jimmy, to let him know. Jimmy Novak is, of course, Castiel's vessel, and so Cas brings along the Winchesters when he goes to visit Claire and find out what she's been up to.
Last seen in The Hunter Games, Claire has found a lead on the fate of her mother, Amelia (Leisha Hailey), that points to a low-life called Ronnie Cartwright (Russell Porter), who the Winchesters learn was working for a local faith healer, Peter Holloway (Treva Etienne).
It turns out that Holloway is actually an ancient rogue angel, feeding on the souls of captive humans.
But in all honesty, the story of Holloway plays second-fiddle in Angel Heart to the continuation of the Claire/Castiel character arc, which develops beautifully.
Claire also gets to spend some quality time with both Sam and Dean, learning more about the hunter's life from them both, their motivations, the cost and the rewards of the path they've chosen.
In recent weeks it appears that Season Ten has finally turned a corner (albeit with only a handful of episodes to go) as Angel Heart is a fantastic blend of the monster-of-the-week format with character development and acknowledgements of the season arc (ie as manifested in Dean's anger issues).
The episode builds to a powerful pair of scenes, one that tugs at the heartstrings, featuring Amelia and Jimmy, and one that, while wrapping up this stage of the Castiel/Claire storyline, opens the door to great possibilities in the future (name-checking Sheriff Jody Mills as it does).
This is the episode where I believe Claire has finally proved herself a worthy addition to the ever-expanding Supernatural family and I look forward to the character's return and continued growth.