We review recent work on fluid-solid and solid-solid phase transitions in soft matter systems such as colloidal suspensions and star polymer solutions. Starting from a given interparticle pair potential we predict the corresponding phase diagrams using computer simulations, cell theory, and density functional theory. When possible, the results are compared with experimental data. In particular, we discuss the following aspects: a cascade of freezing transitions for confined colloids, stable one-component quasicrystals for charged colloids, reentrant melting and anisotropic solid phases for star polymer solutions and reentrant nematic ordering for suspensions of the tobacco-mosaic virus. ©2000 American Institute of Physics.