In this talk, I will review some results on the crystallization conjecture, that is, the mathematical proof of the fact that, under appropriate conditions, interacting particles place themselves into periodic configurations. I will first review classical models at zero temperature, in which few results have been proved. Apart from the question of the emergence of periodicity, determination of the optimal lattice, in link with special functions, will be addressed. Then, some problems regarding the quantum case, in which the notion of crystalline order needs to be defined in a different way. Similarities with positive temperature classical models will be outlined. This is a joint work with M. Lewin (Univ. Paris Dauphine).