Granular materials are an intriguing phase of matter. They can support stresses like a solid, but can also flow down a slope like a liquid. They compress under tapping, but dilate under shearing. Granular materials have fascinated the research community for centuries, but are still not fully understood. A granular statistical mechanical formalism was introduced a quarter of a century ago. However, it is still very much a theory in evolution. In this thesis, we present a few developments of the theory, which make it more rigorous and testable. We adjust the original formalism by replacing the volume function by a more suitable connectivity function. We identify the structural degrees of freedom as the edges of a spanning tree of the contact network graph. We extend the formalism to include constraints on these degrees of freedom and correlations between them. We combine between this formalism and the better established stress ensemble, and then derive an equipartition principle and an equation of state, relating the macroscopic volume and boundary stress to the analogue of the temperature, the contactivity. This makes the theory testable by macroscopic measurements. We then address two application-orientated problems, involving the porous media made by consolidated granular materials. First, we present a scheme to design porous fuel cell electrodes such that the three-phase boundary (TPB) is maximised. These electrodes are made of sintered bi-disperse powders, and the longer their TPB the more efficient the fuel cell. Using a systematic analysis for a commonly used set of given constraints, we find optimal design parameters that yield a TPB that is three times longer than the conventional design under the same constraints. Then, we focus on transport in the pore space of such materials. We study the diffusion of finite-size particles in porous media, and what makes them anomalous. Having pinned-down the causes for sub-diffusion, we develop a continuous-time random walk-based model that predicts correctly the anomaly parameter.