The Moon is a geological history book, preserving information about the history of the Solar System, including the formation and early evolution of the terrestrial planets and their bombardment histories, as well as providing insight into other fundamental Solar System processes. These topics form the basis for science “of the Moon”, but the lunar surface is also a platform for science “on the Moon” and “from the Moon”—including astronomical observations, fundamental physics, and life science investigations. Recently, the Moon has become a destination for technology research and development—in particular for developing in situ resources, human exploration, and habitation, and for its potential use as a waypoint for the human exploration of Mars. This paper, based on recommendations originally proposed in a White Paper for ESA’s SciSpacE strategy, outlines key lunar science questions that may be addressed by future space exploration missions and makes recommendations for the next decades.