After the adoption of “The 2030 Agenda for Sustainable Development” by the UN General Assembly in 2015, the UN Committee on the Use of Outer Space for Peaceful Purposes included in its agenda an item on the development of the Space-2030 plan. It highlighted one of the most important issues that requires increased attention from the world community - regulation of the research, development and use of space resources. The existing legal regime of outer space and celestial bodies is based on the principles laid down in the 60–70s of the last century, and in many aspects it does not meet the modern needs of the community. Based on the analysis of the modern international legal regime of outer space and celestial bodies, the article identifies the legal problems that arise when considering the issue of mining on the Moon and other celestial bodies. © Springer Nature Switzerland AG 2020.