The first goal of this expository talk is to introduce and describe two classical mathematical models of flow and deformation, one is `parabolic', the other is `elliptic'. These are joined to describe fluid flow through deformable porous media as an initial-boundary-value problem for the Biot system of partial differential equations. In the next generation, the boundary conditions of this system are joined with a unilateral constraint of Signorini type. Variational methods are used to reduce the system to a single implicit nonlinear evolution equation in Hilbert space for which the solvability of the initial-value problem can be resolved. We focus on the `structure' of the abstract problem and show that it is `parabolic' with corresponding `regularizing' properties.