The son of professional musicians, Genualdi grew up in Connecticut. His formal training began at age 11 with Broadus Erle. Three years later he enrolled at The North Carolina School of the Arts studying violin with Vartan Manoogian. Upon graduation, he was admitted to the Curtis Institute of Music where he continued his violin studies with Jascha Brodsky and Ivan Galamian. During his years at Curtis he formed a lifelong friendship with Felix Galimir. Subsequently he was awarded the Wardwell and Silliman Fellowships at Yale University.

Throughout his career Joseph Genualdi has specialized in chamber music and contemporary music. He has worked closely with many of the most notable composers of the 20^th and 21^st centuries, often commissioning, premiering and recording their works. They have included Richard Wilson, Chen Yi, Pierre Boulez, Esa-Pekka Salonen, John Corigliano, John Harbison, George Perle, David Diamond, Augusta Reade Thomas, Ellen Taaffe Zwillich, and Peter Lieberson.

He has been the founding first violinist of The Muir String Quartet and Chicago String Quartet. He was a founder of The Chicago Chamber Musicians and toured for ten years with the Los Angeles Piano Quartet. With those groups he has received numerous honors including The Naumburg Award, The Concours d’Evian Gold Medal, The Grand Prix du Disque, and a Grammy Finalist award.

Genualdi has participated in many festivals including Skaneateles, Spoleto (Italy), Ravinia, Taos, Affinis (Japan), Kneisel Hall, Euro Arts, Bravo Colorado, Angel Fire, Nîmes (France),Cheltenham and Marlboro. An enduring affiliation was with the Marlboro Festival and Rudolf Serkin, a guiding influence on his career. His other mentors have included Menahem Presler, Oscar Shumsky, Raphael Hillyer and Mieczysław Horszowsky.