Hogwood conducted a considerable amount of opera. He made his operatic debut in 1983, conducting "Don Giovanni" in St. Louis, Missouri. He worked with Berlin State Opera; La Scala, Milan; Royal Opera Stockholm; the Royal Opera House at Covent Garden, Chorégies d'Orange and Houston Grand Opera. With Opera Australia, he performed "Idomeneo" in 1994 and "La Clemenza di Tito" in 1997. In 2009, he returned to the Royal Opera House to conduct the Orchestra of the Age of Enlightenment in Purcell's "Dido and Aeneas", and Handel's "Acis and Galatea". 2009 also saw him conducting Stravinsky's "The Rake's Progress" at the Teatro Real in Madrid, in a production directed by Robert Lepage. In late 2010 and early 2011, he conducted a series of performances of Mozart's "The Marriage of Figaro" at Zurich Opera House.