A priori crystal structure prediction techniques have been used to explore the phase diagrams of hydrides of main group elements under pressure. A number of novel phases with the chemical formulas MHn, n > 1 and M = Li, Na, K, Rb, Cs; MHn, n > 2 and M= Mg, Ca, Sr, Ba; H n I with n > 1 and PH, PH 2 , PH 3 have been predicted to be stable at pressures achievable in diamond anvil cells. The hydrogenic lattices within these phases display a number of structural motifs including H 2 δ− , H − , H − 3 , as well as one-dimensional and three-dimensional extended structures. A wide range of superconducting critical temperatures, T c s, are predicted for these hydrides. The mechanism of metallization and the propensity for superconductivity are dependent upon the structural motifs present in these phases, and in particular on their hydrogenic sublattices. Phases that are thermodynamically unstable, but dynamically stable, are accessible experimentally. The observed trends provide insight on how to design hydrides that are superconducting at high temperatures.