Neeman has produced a body of profound work of central importance in the core mathematical disciplines of algebraic geometry, topology and K-theory. He has pioneered developments in triangulated categories and their applications. His results on the K-theory of triangulated categories were startlingly original, and completely changed the subject. Neeman’s foundational work, extending the Brown representability theorem, has rendered techniques more powerful; applications include his new treatment of Grothendieck duality. Neeman has made notable contributions to algebraic geometry, especially geometric invariant theory. He has contributed importantly to the interplay of analytic and algebraic invariants of manifolds. His work has been very influential.