The radiative transfer theory has been extensively used in geophysics, remote sensing, and astrophysics for more than a century, but its physical basis had remained uncertain until quite recently. This ambiguous situation has finally changed, and the theory of radiative transfer in random particulate media has become a legitimate branch of Maxwell's electromagnetics. This tutorial review is intended to provide an accessible outline of recent basic developments. It discusses elastic electromagnetic scattering by random many-particle groups and summarizes the unified microphysical approach to radiative transfer and the effect of weak localization of electromagnetic waves (otherwise known as coherent backscattering). It explains the exact meaning of such fundamental concepts as single and multiple scattering, demonstrates how the theories of radiative transfer and weak localization originate in the Maxwell equations, and exposes and corrects certain misconceptions of the traditional phenomenological approach to radiative transfer. It also discusses the challenges facing the theories of multiple scattering, radiative transfer, and weak localization in the context of geophysical applications.