Nonlocal particle systems with Wasserstein interaction arise in electrical engineering (quantization and image processing), economics (optimal location problems), and materials science (crystallization and energy-driven pattern formation). The interaction energy of these systems can be written either in terms of atomic measures and Wasserstein distances or in terms of generalised Voronoi diagrams. In this talk I will present some numerical and analytical results about optimal particle configurations. This is joint work with Filippo Cagnetti, Mark Peletier, Steven Roper, and Florian Theil.