Hydrogels generally consist of a solid network and of a fluid permeating the network. Interactions between the solid and the fluid determine the response of a hydrogel when it is perturbed by, for example, the external mechanical pressure or the external osmotic pressure. The resulting time-dependent dynamics of (de)swelling are characterized by the poromechanical properties of hydrogels: their (visco)elasticity, plasticity and permeability. In this thesis we mainly focus on the characterization of the permeability and elasticity of hydrogels by modelling the dynamics of several (de)swelling processes for synthetic hydrogels and (bio)polymer gels. Also, we delve into the broader problem of compression tests on solids where we investigated a novel compression testing geometry, and we perform a poromechanical study of an industrially relevant phenomenon: the spontaneous expulsion of fluid from low fat mayonnaise.