Arapov began as a pianist, but a disease of the hand ended his performing career and prompted him to enter the Petrograd Conservatory in 1923 to study composition. He took a position as teacher at that university soon after graduation and was appointed professor in 1940. He was head of the composers' section, a board member of the Composers' Union and holds the Red Banner of Labour. His compositions are mainly large-scale and are programmatic with colorful orchestration. He has made field studies of the folk music of Armenia, Georgia, Uzbekistan, China, and Korea, and utilizes these styles in his work.