We present fast numerical algorithms to solve the nonlinear Fokker–Planck–Landau equation in 3D velocity space. The discretization of the collision operator preserves the properties required by the physical nature of the Fokker–Planck–Landau equation, such as the conservation of mass, momentum, and energy, the decay of the entropy, and the fact that the steady states are Maxwellians. At the end of this paper, we give numerical results illustrating the efficiency of these fast algorithms in terms of accuracy and CPU time.