This review paper presents a cohesive collection of thermochemical concepts and linear algebra methods for calculating key thermochemical quantities in computational catalysis. These methods provide tools to combine data from various sources, to integrate experimental and ab initio data, and to convert between different formats. We have defined a notation for evaluating the thermochemistry of adsorbates from DFT data that is consistent with the existing gas-phase thermochemical conventions. All available methods in the literature for converting a set of DFT data into enthalpies of formation were described and explained following the consistent notation. The summary of the methods in Table highlights that they can all be reduced to a simple linear algebra equation to anchor/reference the DFT data and to create a local or global thermochemical network. The difference in the methods is the choice of the anchor/reference species and the source of their enthalpies of formation. This review focused only on the enthalpy of formation at 0 K as it is the foundation of all thermochemistry and has the biggest contribution to the Gibbs free energy. ∆ f H at 0 K can be converted to ∆ f H at other temperatures or to Gibbs free energies of formation by applying finite-temperature corrections through e.g., entropic contributions.