F. S. Boas in the context of "Fellow of the Royal Society of Literature"

The problem play is a form of drama that emerged during the 19th century as part of the wider movement of realism in the arts, especially following the innovations of Henrik Ibsen. It deals with contentious social issues through debates between the characters on stage, who typically represent conflicting points of view within a realistic social context. Critic Chris Baldick writes that the genre emerged "from the ferment of the 1890s... for the most part inspired by the example of Ibsen's realistic stage representations of serious familial and social conflicts." He summarises it as follows:

The critic F. S. Boas adapted the term to characterise certain plays by William Shakespeare that he considered to have characteristics similar to Ibsen's 19th-century problem plays. As a result, the term is also used more broadly and retrospectively to describe any tragicomic dramas that do not fit easily into the classical generic distinction between comedy and tragedy.

In Shakespeare studies, the problem plays are plays written by William Shakespeare that are characterised by their complex and ambiguous tone, which shifts violently between more straightforward comic material and dark, psychological drama. Shakespeare's problem plays eschew the traditional trappings of both comedy and tragedy, and are sometimes cited as early predecessors to the tragicomedy.

The term was coined by critic F. S. Boas in Shakespeare and His Predecessors (1896). Boas' use of the phrase was derived from a type of drama that was popular at the time of his writing, most commonly associated with the Norwegian playwright Henrik Ibsen. In these problem plays, the situation faced by the protagonist is put forward by the author as a representative instance of a contemporary social problem. The term can refer to the subject matter of the play, or to a classification "problem" with the plays themselves.