  Hydrogen is the most abundant element in the universe. It is also the
lightest and as such the most quantum of the elements, in the sense that
quantum tunnelling, quantum delocalisation, and zero-point motion can be
important. For practical reasons most computer simulations of materials have
not taken such effects into account, rather they have treated atomic nuclei as
classical point-like particles. However, it is an exciting time for the theory
and simulation of materials and thanks to significant methodological
developments over the last few decades, nuclear quantum effects can now be
accurately treated in complex materials. In this brief review we discuss our
recent studies on the role nuclear quantum effects play in hydrogen containing
systems. We give examples of how the quantum nature of the nuclei has a
significant impact on the location of the boundaries between phases in high
pressure condensed hydrogen, including a dramatic lowering of the solid to
liquid melting line. We show how nuclear quantum effects facilitate the
dissociative adsorption of molecular hydrogen on solid surfaces and the
diffusion of atomic hydrogen across surfaces; effects that are of relevance to
the catalytic performance of the surfaces. Finally, we discuss how nuclear
quantum effects alter the strength and structure of hydrogen bonds, including
the hydrogen bonds in DNA. Overall these studies demonstrate that nuclear
quantum effects can manifest in many different, interesting, and at times
non-intuitive ways. Whilst historically it has been difficult to know in
advance what influence nuclear quantum effects will have, some of the important
conceptual foundations have now started to emerge.
