The measurement of superconductivity at above 200K in compressed samples of hydrogen sulfide and in lanthanum hydride at 250K is rein- vigorating the search for conventional high temperature superconduc- tors. At the same time it exposes a fascinating interplay between the- ory, computation and experiment. Conventional superconductivity is well understood, and theoretical tools are available for accurate predic- tions of the superconducting critical temperature. These predictions depend on knowing the microscopic structure of the material under consideration, and can now be provided through computational first principles structure predictions. The experiments at the megabar pres- sures required are extremely challenging, but, for some groups at least, permit the experimental exploration of materials space. We discuss the prospects for the search for new superconductors, ideally at lower pressures.CJP is supported by the Royal Society through a Royal Society Wolfson Research Merit award. IE has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 802533), and the Spanish Ministry of Economy and Competitiveness (FIS2016-76617-P). MIE thanks the Max Planck community for invaluable support, and U. Po ̈schl for the constant encouragement
