Rock physics allows us to link geologic processes with geophysical observables through a multiscale integration of data. This integrated analysis is typically done using empirical or theoretical rock-physics models, which are often calibrated with laboratory or field data. With the advent of computational rock physics, a new set of tools can be used to simulate geologic processes and interpret their signatures in the geophysical cross-property domain by computing macroscopic properties on a common or shared rock model. Furthermore, these computational tools allow us to probe, in ways that are nearly impossible with macroscopic physical samples, microscopic (pore-scale) distributions of structural and mechanical heterogeneities, which can have significant effect on macroscopic properties. This in turn can aid in refining conventional theoretical models by accounting for more complex, realistic, and heterogeneous features of porous media, thus taking the theoretical models beyond their limiting, simplifying assumptions and making them more practically applicable. The three key advantages of a computational rock-physics-based modeling approach are (1) use of a common rock model, (2) use of methods based on geologic processes, and (3) use of pore-scale understanding to refine simple yet widely applicable theoretical models. The effects of geologic processes such as compaction, sorting, and diagenesis on elastic and transport property trends not only can be modeled using this computational approach, but pore-scale insights further allow us to critically review simplistic assumptions of commonly used contact-based effective-medium models for these processes.