Nonsymmetric Macdonald polynomials are orthogonal polynomials in several variables, introduced by Macdonald and studied extensively by Cherednik, Knop and others. In this talk we discuss how they grew out of the study of Macdonald's root-system constant term conjectures, and describe a new combinatorial formula for them in the type A case due to M. Haiman, N. Loehr and the speaker.