  The main objective of this Report is to formulate the general theoretical
framework of electromagnetic scattering by discrete random media rooted in the
Maxwell-Lorentz electromagnetics and discuss its immediate analytical and
numerical consequences. Starting from the microscopic Maxwell-Lorentz
equations, we trace the development of the first-principles formalism enabling
accurate calculations of monochromatic and quasi-monochromatic scattering by
static and randomly varying multiparticle groups. We illustrate how this
general framework can be coupled with state-of-the-art computer solvers of the
Maxwell equations and applied to direct modeling of electromagnetic scattering
by representative random multi-particle groups with arbitrary packing
densities. This first-principles modeling yields general physical insights
unavailable with phenomenological approaches. We discuss how the
first-order-scattering approximation, the radiative transfer theory, and the
theory of weak localization of electromagnetic waves can be derived as
immediate corollaries of the Maxwell equations for very specific and
well-defined kinds of particulate medium. These recent developments confirm the
mesoscopic origin of the radiative transfer, weak localization, and
effective-medium regimes and help evaluate the numerical accuracy of widely
used approximate modeling methodologies.
