The pressure variable opens the door towards the synthesis of materials with unique properties, ie. superconductivity, hydrogen storage media, high-energy density and superhard materials, to name a few. Under pressure elements which would not normally combine may form stable compounds, or may mix in novel proportions. Because of this using our chemical intuition developed at 1 atm in order to predict stable phases is bound to fail. In our search for superconducting hydrogen-rich systems under pressure, we have used the XtalOpt evolutionary algorithm to predict stable phases, followed by first-principles calculations of their emergent electronic structures . Our focus has been on the alkali metal polyhydrides, MHn (n > 1 and M = Li, Na, K, Rb, Cs), and the alkaline earth polyhydrides MHn (n > 2 and M = Be, Mg, Ba, Sr). The results of our computational experiments, are helping us to build chemical and physical intuition for compressed solids.