A theory is geometric if in its models, the algebraic closure satisfies the exchange property, and the theory eliminates the infinity quantifier. Examples of geometric theories include strongly minimal, SU-rank 1 and o-minimal theories. We will give an overview of expansions of models of geometric theories with a subset satisfying the density-codensity condition introduced in our joint work with Alexander Berenstein in the settings of algebraically closed subsets (lovely pairs) and algebraically independent subsets (H-structures). We will then discuss some examples of dense-codense expansions intermediate between lovely pairs and H-structures, a number of preservation results, and properties of closure operators induced by such expansions, including connections to linearity and representability of finite matroids.