When it opened in 1974 at the Aldwych Theatre in London, Travesties earned overwhelmingly positive reviews. Critics applauded the play's wit as well as its depth. Wilborn Hampton in his review in the New York Times writes that the play "races forward on Mr. Stoppard's verbal roller coaster, leaving one dizzy yet exhilarated by its sudden semantic twists, turns, dips, and loops." Clive Barnes's review in the New York Times suggests Stoppard" has constructed a whole ballet of words, wit and oddly disturbing literary echoes." T.E. Kalem in Time insists the play "blaz[es] with wit, paradox, parody, and, yes, ideas. It is exhilaratingly, diabolically clever."

Susan Rusinko in her article on Stoppard for Twayne's English Authors Series Online claims Stoppard's "dazzling language" is "sheer magic" and that the entire play contains "the most intoxicating reinvention of language on the modern English stage."