Multipath scattering environments are associated with many unique and interesting propagation characteristics. One of the most important features in such environments is the rich spatial diversity of the received signals or electromagnetic (EM) fields. Another prominent one is the diffusive behavior of waves regarding their power decay. Both of them are studied in this work. The spatial diversity, as well as polarizations, of the EM fields allows the advantage from the spatial domain to be exploited, which is probably best exemplified by the Multiple-Input-Multiple-Output (MIMO) systems. This study is interested in the question of how much advantage a MIMO system can possibly obtain spatially, and it is studied from a more fundamental perspective by investigating the degrees of freedom (DOF) provided by the information-carrying EM waves. Because the EM DOF is an antenna-independent figure-of-merit, it can be used to measure the maximum information delivery capability, hence the capacity upper bound, of an actual MIMO system. In this work, an EM DOF definition with relevant physical interpretation and rigorous mathematical groundwork is identified; an efficient numerical technique of evaluating the DOF number is developed; and the technique is applied to random multipath media modeling the environments encountered in real life. The outcomes reveal significant insights about the dependence of EM DOF number on the system and the surrounding environments. The diffusion of waves in multipath environments is studied with a focus on the applicability of the transport theory to received power prediction. The limitations to this model as imposed by a number of physical factors of the multipath media are explored through a full wave approach, and the conditions under which the wave behavior becomes diffusive enough for the model to be applicable with sufficient accuracy are determined. With this done, attempts are made to develop a multipath propagation model in the double-angular domain by combining the transport theory and the frequently used uncorrelated scattering assumption, which is also tested in this work. The developed model relates the multipath components in a system directly to its configuration parameters, which makes it very convenient to estimate the propagation characteristics of the waves based on the knowledge about the environments. Potential applications can be found in many wireless communications issues, including evaluating the EM DOF without solutions to scattering problems.