Hydrogen is the most abundant element. It is also the most quantum, 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 nuclei as classical particles. However, thanks to methodological developments over the last few decades, nuclear quantum effects can now be treated in complex materials. Here we discuss our 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. We show how nuclear quantum effects facilitate the dissociative adsorption of molecular hydrogen on solid surfaces and the diffusion of atomic hydrogen across surfaces. Finally, we discuss how nuclear quantum effects alter the strength and structure of hydrogen bonds, including those in DNA. Overall these studies
demonstrate that nuclear quantum effects can manifest in different, interesting, and 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.