Statistical and relaxation properties of dusty plasmas are studied numerically and analytically. The fluctuation electrodynamics of dusty plasmas is determined taking into account the dynamics of charging processes associated with plasma currents. The influence of grain charging on the effective interaction between dust particles is discussed. Grain attraction and dusty crystal formation are shown to be possible. The results of numerical simulation of dusty plasma relaxation caused by grain charging and plasma-layer expansion are presented in detail. Monte Carlo simulations are used to prove the existence of dust particle effective attraction within a model with constant grain charge.