From Poetry Wiki
Verse drama is any drama written as verse to be spoken; another possible general term is poetic drama. For a very long period verse drama was the dominant form of drama in Europe (and was also important in non-European cultures). Greek tragedy and Racine's plays are written in verse, as is almost all of Shakespeare's drama, and Goethe's Faust.
Verse drama is particularly associated with the seriousness of tragedy, providing an artistic reason to write in this form, as well as the practical one that verse lines are easier for the actors to memorise exactly. In the second half of the twentieth century verse drama fell almost completely out of fashion with dramatists writing in English (the plays of Christopher Fry and T. S. Eliot being possibly the end of a long tradition).
Dramatic verse occurs in a dramatic work, such as a play, composed in poetic form. The tradition of dramatic verse extends at least as far back as ancient Greece. It was probably used by Greek playwrights such as Euripides for incantatory effect and to make long passages easier to memorize.
The English Renaissance saw the height of dramatic verse in the English-speaking world, with playwrights such as Ben Jonson, Christopher Marlowe and William Shakespeare developing new techniques, both for dramatic structure and poetic form. Though a few plays, such as A Midsummer Night's Dream, feature extended passages of rhymed verse, the majority of dramatic verse is composed as blank verse; there are also passages of prose.
Dramatic verse began to decline in popularity in the nineteenth century, when the prosaic and conversational styles of playwrights such as Henrik Ibsen became more prevalent, and were adapted in English by George Bernard Shaw. Verse drama did have a role in the development of Irish theatre.
The closet drama
A important trend from around 1800 was the closet drama: a verse drama intended to be read from the page, rather than performed. Lord Byron and Shelley, as well as a host of lesser figures, devoted much time to the closet drama, in a signal that the verse tragedy was already in a state of obsolescence. That is, while poets of the eighteenth century could write poetic dramas sincerely, the public taste for new examples was already moving away by the start of the nineteenth century, and there was little commercial appeal in staging them. Instead, opera would take up verse drama, as something to be sung: it is still the case that a verse libretto can be successful. Verse drama as such, however, in becoming closet drama, became simply a longer poetic form, without the connection to practical theatre and performance.
According to Robertson Davies in A Voice From the Attic, closet drama is "Dreariest of literature, most second hand and fusty of experience!". But indeed a great deal of it was written in Victorian times, and afterwards, to the extent that it became a more popular long form at least than the faded epic. Prolific in the form were, for example, Michael Field and Gordon Bottomley.
Dramatic poetry in general
Dramatic poetry is any poetry that uses the discourse of the characters involved to tell a story or portray a situation.
The major types of dramatic poetry are those already discussed, to be found in plays written for the theatre, and libretti. There are further dramatic verse forms: these include dramatic monologues, such as those written by Robert Browning and Alfred Tennyson.