In this paper we shall present a review of a theoretical hydrodynamic framework of compressible SmC* liquid crystals involving a wave vector to represent the layer compression. In practice we shall derive a set of simultaneous non-linear continuum equations which are regarded as an extension of the incompressible case. It is found that the present theory involves 17 + 4* (*:chiral) elastic constants and 25 viscosity coefficients for compressible SmC* phase, which are eventually reduced to 9 + 2* and 20, respectively, for incompressible smectics. It is also shown that the layer normal unit vector and the compressibility scalar function have to be related to each other through a Lagrange multiplier so as to satisfy the irrotational constraint corresponding to the conservation law of the number of layers as was assumed in the incompressible smectics. (C) 2004 Elsevier B.V. All rights reserved.