David Rosen's research has centered on 19th-century and early 20th-century Italian music, primarily Verdi and Puccini, although he has also written about opera theory and Mozart piano concertos. He edited Verdi's Messa da Requiem in The Works of Giuseppe Verdi, the critical edition, and is the author of the Cambridge Music Handbook about that work. He has long been interested in the staging manuals (disposizioni sceniche or livrets de mise en scène) and other sources that help us reconstruct the visual aspects of 19th-century opera, and he co-authored a volume dedicated to the disposizione scenica of Verdi's Un ballo in maschera. A recurring theme in his work is compositional decision-making.

Until recently he was editor of The Verdi Forum (formerly The Verdi Newsletter, the publication of the American Institute for Verdi Studies) and is now on its editorial board, as well as on the advisory board of the Fondo Leoncavallo (Locarno, Switzerland) and of the Centro studi Giacomo Puccini (Lucca, Italy). He has served the American Musicological Society on the national level (AMS Council, Einstein Award Committee, and Program Committee) and the chapter level (chair of the NY-St. Lawrence chapter and Secretary-Treasurer of the Midwest chapter).

The courses he teaches range from those designed for undergraduates not majoring in music (e.g., Opera, Musical Romantics, The Piano and its Music) to graduate seminars (e.g., Verdi, Puccini, Britten's Operas, The Problem of the "Composer's Intentions"). He recently served as Director of Graduate Studies for three years.