Coming off of his win at Sunday's Golden Globes, Firth was nominated for leading actor and is up against Jesse Eisenberg (The Social Network), Jeff Bridges (True Grit), Javier Bardem (Biutiful) and James Franco (127 Hours).
Black Swan received 12 nominations, including one for best film. Joining the Darren Aronofsky film in the category is Inception, The King's Speech, The Social Network and True Grit. Also nominated from the psychological thriller is Natalie Portman in the leading actress category and Barbara Hershey in the supporting actress category.
The BAFTAs will be handed out on Feb. 13 at the Royal Opera House in London.
See the full list of nominations here.