The recent increase in the production of high value-added, low-volume specialty chemicals and biochemicals has generated a renewed interest in batch processing technologies. Batch distillation is an important unit operation in the batch processing industry and is most widely used. The flexibility of batch distillation, combined with the inherent unsteady nature of the process, poses challenging design and operation problems. This paper presents a complete review of batch distillation starting from the very first analysis in 1902 by Lord Rayleigh to the current state of the art. The paper will (a) introduce the various operating modes, (b) examine the challenges involved in rigorous modeling of batch distillation column dynamics, (c) provide a hierarchy of models of varying complexity and rigor, (d) present approaches to the optimal design and control of batch distillation columns and highlight the differences vis-g-vis continuous distillation columns, (e) analyze complex systems, (f) present methods to synthesize complex column designs, and (g) present an overview of available software packages for design, optimization, and control of batch distillation columns.