Particles interacting via purely repulsive soft-core potentials can spontaneously aggregate, despite repelling each other, and form periodic crystals of particle clusters. We studied this phenomenon - relevant to colloidal or polymer solutions - for passive (Brownian) and active (self-propelling) particles at two levels of description: performing numerical simulations of the discrete particle dynamics, and by linear and nonlinear analysis of the corresponding Dean-Kawasaki equations for the macroscopic particle density. In this seminar, I will explain what are the mechanisms of the instability leading to clustering which turn out to be the interplay between diffusion or self-propulsion, the intracluster forces and the forces between neighboring clusters.