Abstract: We introduce the crystallization problem and its connection to the Wulff problem. We focus on the minimization of Heitman-Radin potential energies for configurations of N particles. Besides identifying the asymptotic Wulff shapes through Gamma-convergence, we introduce the concept of fluctuation and discuss optimal fluctuations for quasiminimizers proving in particular the well-known N^{3/4} conjecture for minimizers on planar lattices. Our technique combines the sharp quantitative Wulff inequality with a notion of quantitative closeness between discrete and continuum problems. We eventually discuss some recent result on the three dimensional case obtained in collaboration with Gian Paolo Leonardi (Trento) and Leonard Kreuz (Münster).