Rundell grew up in Bloomington, Minnesota. He attended Northwestern University, where he studied conducting with John Paynter and trombone with Frank Crisafulli. Rundell earned a fellowship to continue his conducting studies with Timothy Reynish at the Royal Northern College of Music in Manchester, England, and he has been based for much of his career in that city, joining the RNCM faculty and continuing to teach there as of the early 2020s. He made his recording debut in 1995, conducting the Royal Northern College of Music Wind Orchestra on an album of music by composer John McLeod, Visions of the North. He made several more albums with that ensemble, including a series devoted to the wind music of Percy Grainger.
In addition to teaching, Rundell found himself in demand as a guest conductor. He earned a reputation for mastering difficult scores quickly, conducting the Barcelona Symphony Orchestra in Leonard Bernstein's three-hour Mass with just 48 hours' notice. Rundell has a large repertory extending from the Classical period to contemporary works, and his projects have extended into jazz, rock, and world music as well. He has appeared as a guest with such groups as the Gulbenkian Orchestra of Lisbon, the SWR-Sinfonieorchester Baden-Baden, and the NDR Radiophilharmonie in Hannover, as well as all of the BBC Orchestras and several other major orchestras in Britain. Often he has been invited back to lead orchestras he has conducted. Rundell specializes in 20th century opera, having conducted such works as Benjamin Britten's Albert Herring and The Turn of the Screw, Maurice Ravel's L'Heure Espagnole and L'enfant et les sortilèges, and Leoš Janácek's Káta Kabanová and The Cunning Little Vixen. He is strongly committed to contemporary music in a wide range of styles and has led world premieres of works by composers as diverse as Louis Andriessen, Steve Reich, and James MacMillan. Rundell has also worked across genre boundaries, with a list of collaborators that includes jazz saxophonist Wayne Shorter, rock songwriter Elvis Costello, and kora player Toumani Diabaté. By 2022, his recording catalog encompassed more than 50 items, including most recently guitarist Xuefei Yang's Magna Carta, featuring works by John Brunning, on which he conducted the Royal Liverpool Philharmonic Orchestra. ~ James Manheim, Rovi