The behaviour of compressible sediments and filter cakes is of significant fundamental interest and widespread practical importance; for example, in the area of solid-liquid separation engineering. In this paper, we review briefly recent progress made in the characterisation and modelling of the behaviour of compressible particulate gels using an approach which we shall for convenience call "compressional rheology", following de Kretzer et al. [R.G. de Kretzer, D.V. Boger. P.J. Scales, Compressive Rheology: An Overview, Rheol. Rev., 1 2003, 125-166 (British Society of Rheology)] and others. The bulk of the paper will be concerned with one-dimensional consolidation under hydrostatic loading in one guise or another, modelled using extensions of an approach suggested by Philip and Smiles [J.R. Philip, D.E. Smiles. Macroscopic analysis of the behavior of colloidal suspensions, Adv. Colloid Interface Sci. 17 (1) (1982) 83-103] and Buscall and White [R. Buscall, L.R. White, The consolidation of concentrated suspensions. Part 1. The theory of sedimentation. J. Chem. Soc. Faraday Trans. 183 (3) (1987) 873-891]. One-dimensional compressional rheology has been used to model processes Such as filtration and sedimentation, and the field is being extended to centrifugation, drying and Vacuum filtration currently. It is however the case that by no means all experiments and applications can be treated as one-dimensional, even approximately, and so towards the end the paper we anticipate and discuss the challenge of generalising to arbitrary loadings and higher-dimensional flows. (C) 2009 Published by Elsevier B.V.