We look at what astronomy from the Moon might be like over the next few decades. The Moon offers the possibility of installing large telescopes or interferometers with instruments larger than those on orbiting telescopes. We first present examples of ambitious science cases, in particular ideas that cannot be implemented from Earth. After a general review of observational approaches, from photometry to high contrast and high angular resolution imaging, we propose as a first step a 1-metre-class precursor and explore what science can be done with it. We add a proposal to use the Earth–Moon system to test the quantum physics theory.This article is part of a discussion meeting issue 'Astronomy from the Moon: the next decades (part 2)'.