Black comedy, also known as black humour and dark comedy, is traditionally edgy in style and usually mocks serious subject matter. Topics can range from politics to religion and even death (gallows humour). By its very nature, black comedy will entertain some while offending others.
The term in its current use was coined by André Breton, the main theoretician of the French surrealist movement (humour noir) in his work Anthology of Black Humour (1940).
While a legitimate theatre genre, works are few in number. The Book of Mormon is a fine example as it mocks the Church of Jesus Christ of Latter-day Saints in a lighthearted manner. The genre is sometimes associated with satire, farce and even absurdism (Rosencrantz and Guildenstern are Dead by Tom Stoppard).
Black Comedy Theatre Resources
25+ examples of black comedy in plays and musical theatre works.
Historical analysis of the origins of the term in literature and the theatre.
Useful explanation of the term from TV Tropes with multiple examples of black humour in a variety of formats including advertising, comic books, film, literature, theatre etc.
Wikipedia entry including etymology and history of the term.
Rotten Tomatoes 60 best movies belonging to the genre.
Brief historical overview from Encyclopaedia Britannica.
Examples of plays belonging to the genre.
Explanation of how the genre operates in the field of literature.
Handy explanation of movie conventions with several film examples.