  The theoretical exploration of the phase diagrams of binary hydrides under
pressure using \emph{ab initio} crystal structure prediction techniques coupled
with first-principles calculations has led to the \emph{in silico} discovery of
numerous novel superconducting materials. This Perspective article focuses on
the alkaline earth and rare earth polyhydrides whose superconducting critical
temperature, $T_c$, was predicted to be above the boiling point of liquid
nitrogen. After providing a brief overview of the computational protocol used
to predict the structures of stable and metastable hydrides under pressure, we
outline the equations that can be employed to estimate $T_c$. The systems with
a high $T_c$ can be classified according to the motifs found in their
hydrogenic lattices. The highest $T_c$s are found for cages that are
reminiscent of clathrates, and the lowest for systems that contain atomic and
molecular hydrogen. A wide variety of hydrogenic motifs including 1- and
2-dimensional lattices, as well as H$_{10}^{\delta-}$ molecular units comprised
of fused H$_5^{\delta-}$ pentagons are present in phases with intermediate
$T_c$s. Some of these phases are predicted to be superconducting at room
temperature. Some may have recently been synthesized in diamond anvil cells.
