The idea of collecting solar energy in space and beaming this energy to Earth has been around since the late 1960s. Based on existing technologies, space solar power (SSP) could become an economically viable alternative to today's commercial energy sources within the next thirty years. This article describes the legal environment for SSP and examines whether the current available legal tools are sufficient to protect the interest of both SSP operators and the public. It examines the international regulatory framework, European Union law and the national legal regimes of the United States and China – both major players in space and both having SSP ambitions. It concludes that one of the main legal challenges will be how to frame liability, from the perspective of both the operator and the public. The article provides suggestions on how to frame liability for SSP.