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An important class of machine scheduling problems is characterized by a no-wait or blocking production environment, where there is no intermediate buffer between machines. In a no-wait environment, a job must be processed from start to completion, without any interruption either on or between machines. Blocking occurs when a job, having completed processing on a machine, remains on the machine until a downstream machine becomes available for processing. A no-wait or blocking production environment typically arises from characteristics of the processing technology itself, or from the absence of storage capacity between operations of a job. In this review paper, we describe several well-documented applications of no-wait and blocking scheduling models and illustrate some ways in which the increasing use of modern manufacturing methods gives rise to other applications. We review the computational …