Nonlocal shape optimization problems involving interaction energies with competing repulsive and attractive terms are of interest in a variety of applications and have been extensively studied in the last decades in the mathematical community. In this short course I will focus on nonlocal energies defined on sets with prescribed mass, where the repulsive interaction is of Riesz type and the attractive interaction is a power law. I will first review some results in the isotropic case, that is, when both the repulsive and the attraction kernels are radially symmetric. In this setting existence of minimizers typically fails for small mass, whereas the unique minimizers are balls for large mass. I will then discuss some recent advancements for a class of anisotropic kernels and show how the occurrence of a critical mass for existence is related to the shape of minimizers when considering the energy on the larger class of measures with prescribed mass. If time permits, I will discuss some open questions and future perspectives.