There can be no exact classification because the genres seem to merge or converge at times. Taking Shakespeare as a starting point one could say we have Tragedy; Hamlet, Macbeth, Othello, King Lear: Comedy; Merchant of Venice, A Midsummer Night’s dream, As you like it and others, Tragi-comedy, The Tempest, History; Richard the second, Roman plays; Julius Caesar
Restoration Comedy; The Way of the World, Farce; The Importance of being earnest, Musical; Pygmalion, Psychological drama; Hedda Gabler, Realist drama; Chekov’s Cherry Orchard, Alienation drama; Bertolt Brecht’s Mother Courage, Existentialist theatre; Eugene Ionesco’s Six Characters in search of an author, The theatre of the absurd; Samuel Becket’s, Waiting for Godot.
Drama since the days of the Greek tragedy has undergone phenomenal changes both in form and in the way the story is narrated. Since drama is a performing medium unlike the poem, the novel or the short story, a drama tends to be action centred. The development of modern thought and philosophy has influenced drama extensively and in the 20th century drama in Literature became one of the most powerful weapons to produce debate, awe or emotion in the audience.