The principal mechanisms of classical diffusion (due to binary collisions) of a partially-ionized plasma in a homogeneous magnetic field are examined. As a result of anisotropy of the transport coefficients of charged particles the problem proves to be far more complicated than the well-known problem of ambipolar diffusion in the absence of a magnetic field. The evolution of diffusion in this case is determined primarily by eddy currents flowing in the plasma. The circuit for these currents can be completed both through the background plasma giving rise to depletion regions, and by the conducting walls of the container of the plasma (the short-circuit effect). Ambipolar diffusion which occurs when the electron and ion fluxes are equal at every point can be realized only in exceptional cases. Experiments are described in which the short-circuit effect and ambipolar diffusion were observed. Using different boundary conditions it was possible to vary the diffusion rate of the plasma by two or three orders of magnitude, and this presents the possibility of controlling the local parameters of the plasma. This review has taken into account references up to July, 1979.