Deep eutectic solvents (DESs) are binary or ternary mixtures of compounds that possess significant melting point depressions relative to the pure isolated components. The discovery of DESs has been a major breakthrough with multiple fields benefitting from their low cost and tunable physiochemical properties. However, tailoring DESs for specific applications through their practically unlimited synthetic combinations can be as much a hindrance as a benefit given the expense and time-required to perform large-scale experimental measurements. This emphasizes the need for fast computational tools capable of making accurate predictions of DES physiochemical properties exclusively from molecular structure. Yet, these systems are not trivial to model or simulate at the atomic level given their exceedingly nonideal behaviors, asymmetry of components, and the complexity of their molecular electrostatic interactions. Despite the challenge, computational reports featuring quantum mechanical (QM) methods have provided significant understanding into the relationship between the melting point depression and the unique and complex hydrogen bond network present in DESs. Classical molecular dynamics (MD) methods have examined bulk-phase solvent organization in conjunction with thermodynamic and transport properties. Machine learning (ML) algorithms have shown great potential as structure-property prediction tools. Overall, this review highlights computational accomplishments that have meaningfully advanced our understanding of DESs and strives to give the reader a sense of the overall strengths and drawbacks of the methodologies employed while hinting at promises of advances to come.