The fundamental quantity used to describe radiative transfer is the radiance or specific intensity. For unpolarized descriptions of surface scattering, the radiance is used in conjunction with the bidirectional reflectance distribution function (BRDF) defined by Nicodemus. Unfortunately, the BRDF does not describe polarization effects. In recent years, polarized descriptions of surface scattering have been developed, but the relationship between the BRDF and the polarized descriptions of surface scattering have not been published. The unpolarized description of surface scattering, which involves radiances and BRDFs, is extended to properly describe polarization effects. The concepts of radiance, irradiance, intensity, and radiant power are redefined as vector quantities. The intensity vectors are defined as conventional Stokes vectors and as the modified Stokes vectors adopted by Ishimaru, Ulaby, and others. The BRDF and directional reflectance matrices are defined and expressed in terms of the amplitude scattering matrix elements and in terms of the intensity scattering or phase matrix. The relationships between the unpolarized and polarized BRDFs and directional reflectances are discussed.