A review of computational studies on the structures, bonding and reactivity of rhodium σ-alkane complexes in the solid state is presented. These complexes of the general form [(R2P(CH2)nPR2)Rh(alkane)][BArF 4] (where ArF = 3,5-(CF3)2C6H3) are formed via solid/gas hydrogenation of alkene precursors, often in single-crystal-to-single-crystal (SC-SC) transformations. Molecular and periodic density functional theory (DFT) calculations complement experimental characterisation techniques (X-ray, solid-state NMR) to provide a detailed picture of the structure and bonding in these species. These σ-alkane complexes exhibit reactivity in the solid state, undergoing fluxional processes, and access different alkane binding modes that link to C-H activation and H/D exchange. The mechanisms of several of these processes have been defined using periodic DFT calculations which provide excellent quantitative agreement with the available experimental activation barriers. A comparison of computed results derived from periodic DFT calculations, where the full solid-state environment is taken into account, with simple model calculations using the isolated molecular cations highlights the importance of modelling the solid state to reproduce the structures of these alkane complexes. The solid-state environment can also have a significant impact on the computed reaction energetics.