Dewatering of the residues produced by wastewater treatment has received increased attention in recent years as a result of increased sludge quantities and increased energy costs. While a wide variety of different processes are used for sludge dewatering, all involve flow of liquid through porous media in response to a pressure gradient. Quantitative evaluation of the rate at which liquid can be removed from sludge solids in various dewatering devices is complicated by the fact that most wastewater sludges are highly compressible — that is, the solid structure of the sludge deforms under applied pressure resulting in reduction in sludge permeability. In this review, theories of flow through compressible porous media are summarized (with special attention to developments since P. C. Carman's 1938Fundamental Principles of Industrial Filtration),comparisons between theories are drawn, and theoretical inadequacies are identified. The application of theory to wastewater sludge management practice is considered, and discrepancies between theory and practice are discussed. Characteristics of common sludges and common sludge dewatering equipment are reviewed.