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The question of how to define the work performed on a quantum system undergoing a thermodynamic process has recently received much attention, particularly in the context of nonequilibrium work relations. The first part of my talk concerns the link between classical and quantum definitions of work for a thermally isolated system. I will show that the quantum work distribution can be approximated accurately in terms of classical trajectories that interfere coherently, via pathintegral phases, and I will extend this result to describe tunneling into the classically forbidden region. These results provide justification for a definition of quantum work based on initial and final projective energy measurements. The second part of the talk concerns the work performed on a quantum system that is weakly coupled to a thermal environment. The coupling strength is presumed to be sufficient to bring about decoherence  thereby altering the quantum work distribution  but insufficient to allow for substantial energy exchange between system and environment. I will argue that in this situation the quantum work is again naturally defined as the difference between initial and final projective energy measurements, and that nonequilibrium work relations remain valid within this scheme. 