Configuration spaces of points have been studied extensively as interesting examples of topological spaces. Configuration spaces of particles are a natural generalization which arise naturally as the energy landscape of a hard spheres system in statistical physics. Although they arise naturally in mathematics and physics, little is known about their topology. I’ll overview in this talk recent progress in understanding these spaces, focusing on the notion of “phase transitions”. The talk will be largely self contained and I will not assume any particular topological prerequisites. This is based on joint work with a number of collaborators, including Hannah Alpert, Ulrich Bauer, Robert MacPherson, and Kelly Spendlove.