The extent to which we can describe reliably the nuclear equation of state in different thermodynamical domains determines whether we can make the most of new observational data on neutron-star properties, computationally demanding supernova simulations, and even the anticipated detection of gravitational waves - with important implications for diverse fields of physics. In this seminar I will focus on the description of baryonic matter at sub-saturation densities and low temperatures, where nuclei (or clusters) and a gas of nucleons are expected to coexist and interact with each other and with surrounding leptons. I will present a simple, but microscopically motivated model for heavy clusters, and a potentially unified description of light and heavy clusters. I will discuss the relevance of such studies in the evolution of core-collapse supernovae and give perspectives for future developments.
