The use of high pressure in physics provides access to unusual chemistry, rich phase behaviour, and various interesting phenomena. One of the most sought after phenomena of recent years is high-temperature superconductivity, which has been predicted in solid hydrogen and experimentally verified in numerous metal hydrides.

This thesis adds to the knowledge of these high-pressure light-atom systems and introduces new tools for predicting their superconducting properties. It showcases the calculation of an anharmonic phase diagram of solid hydrogen, demonstrates that current theoretical techniques can produce structures and superconducting critical temperatures (Tc) in agreement with experiment for the record-holding binary hydride LaH10, and reveals a metastable hexagonal phase of this material that provides an explanation for recent experimental observations. It also addresses the real need to reduce the operational pressure of superconducting hydrides and offers a solution through the use of machine learning methods, leading to the discovery of several superconductors inhabiting favourable regions of P-Tc space.

It is common for papers in this field to focus on the stability and superconductivity of a limited number of metal hydrides, largely because the electron-phonon calculations involved are computationally expensive and because it is not clear which hydrides are potential high-Tc candidates before performing these calculations. This drastically slows down the rate of discovery. The work presented in this thesis provides a solution to this problem; by identifying physically motivated descriptors from scattering theory and density of states calculations, we are able to construct a model for Tc and therefore obtain a method for cheaply identifying the most promising candidate structures. Incorporating this screening step into a high-throughput workflow allows us to study superconductivity in binary hydrides from across the whole periodic table, resulting in one of the most comprehensive studies of superconductivity in binary hydrides ever produced and leading to the identification of several above- and near-room-temperature candidates.

The methods developed in this thesis could be expanded to other classes of materials, including ternary hydrides and other light binaries, and used as a guide to designing high-throughput workflows for other material properties. The findings may bring us closer to the ultimate goal of first-principles material design.