A new era of lunar exploration has begun with participation of all major space agencies. This activity brings opportunities for revolutionary science experiments and observatories on the Moon. The idea of a lunar gravitational-wave detector was already proposed during the Apollo programme. The key characteristic of the Moon is that it is seismically extremely quiet. It was also pointed out that the permanently shadowed regions at the lunar poles provide ideal conditions for gravitational-wave detection. In recent years, three different detector concepts were proposed with varying levels of technological complexity and science potential. In this paper, we confront the three concepts in terms of their observational capabilities based on a first more detailed modelling of instrumental noise. We identify important technological challenges and potential show-stoppers. This article is part of a discussion meeting issue 'Astronomy from the Moon: the next decades (part 2)'.
Keywords: gravitational-wave detection; lunar environment; noise models.