The study of the properties of strong interactions at finite density is one of the most challenging and fascinating tasks in contemporary nuclear physics, as the phase structure of QCD in this regime is expected to be quite rich. In this talk, I will present an overview of some recent results on the characterization of strong interaction matter at finite baryonic and isospin densities within effective field theories and models of QCD, ranging from the study of the possible formation of crystalline phases to the phenomenon of pion condensation. I will also discuss the relevance of the existence of these phases for the physics of compact stellar objects and heavy-ion collision experiments.