The selective conversion of alkanes to high value products remains a monumental catalytic challenge. Significant gaps in our knowledge remain regarding the mechanistic details of alkane activation and the chemical nature of the catalytically active sites for this class of reactions. In this thesis, systematic and thorough first principles studies of alkane activation on several major classes of promising materials, ranging from metal oxide surfaces to metal clusters and single metal atom sites, have provided us with the insight to tackle these open questions. To further expand these findings towards a comprehensive search of catalytically active materials, we developed chemical and catalytic descriptors which can predict these properties at a fraction of the computational cost. We find on oxide surfaces, the homolytic C-H activation pathway is favored, and correlated with the reducibility of the lattice oxygen. We identify hydrogen adsorption energy and vacancy formation as strongly correlated energetic descriptors for C-H activation energy and CH3 adsorption energy, which we use to predict catalytic properties of doped Co3O4 and compositionally diverse perovskite surfaces. To provide a structure-activity link between the oxygen and alkane activation, we developed a generally applicable coordination number descriptor, 'ACN, ' which can quickly predict C-H activation barriers on various oxides. Furthermore, we identify a bulk descriptor, the metal-oxygen crystal orbital Hamilton population, which is correlated to the adsorption energy of radical adsorbates such as hydrogen and methyl. Meanwhile on metal clusters, structural fluxionality plays a pivotal role in catalytic performance. In the model system of Pt10-13, we utilize various structural features to identify Pt10 as a magic number cluster with low fluxionality which can explain its experimental inertness to alkanes. On single atoms, we demonstrate how heterolytic C-H cleavage pathway can be tuned through the metal d-orbital occupation and the substrate electronic band gap. These findings have allowed us to identify promising single atom catalysts with the elusive low-temperature methane activation ability. The work in this thesis aims to provide valuable descriptors and design principles for alkane activation and theoretical predictions of promising catalysts.