We present results, obtained by rigorous computational approaches, for light of $p$- and $s$-polarization scattered from two-dimensional, randomly rough, perfectly conducting, lossy metallic, and dielectric surfaces. The perfectly conducting surfaces we study are characterized by an isotropic power spectrum of the surface roughness and by an anisotropic power spectrum. The mean differential reflection coefficient and the full angular distribution of the intensity of the scattered light are calculated for the perfectly conducting and metal surfaces. From the latter calculations it is found that the computational approach used in these calculations conserves energy in the scattering from a perfectly conducting and from a lossless metal surface with an error that is smaller than $0.5\%$. Finally, we presents results obtained by a numerical, nonperturbative, solution of the reduced Rayleigh equation for the scattering of $p$- and $s$-polarized light from two-dimensional randomly rough, metallic and dielectric surfaces. We show that the results for the metallic surface are in good agreement with results for the same metallic surface obtained by the rigorous computational approach.