Reproducibility is widely considered to be an essential requirement of the scientific process. However, a number of serious concerns have been raised recently, questioning whether today’s computational work is adequately reproducible. In principle, it should be possible to specify a computation to sufficient detail that anyone should be able to reproduce it exactly. But in practice, there are fundamental, technical, and social barriers to doing so. The many objectives and meanings of reproducibility are discussed within the context of scientific computing. Technical barriers to reproducibility are described, extant approaches surveyed, and open areas of research are identified.