Energy resources in outer space, also known as space energy, has been recognized as a promising supplement to conventional energy supplies on Earth, as well as an irreplaceable energy provision for future space explorations. A critical review is conducted in this paper, to identify the most potential space energy resources, to conclude on the current exploitation technologies and to suggest on the challenges and future directions. Space solar power station, also known as SSPS, is presented first as a well-known utilization of space energy, and we go through the international progress, evolution of the collection systems and the thermophotovoltaic systems. The main technical gaps hampering the practical application of SSPS is concluded then to inspire future investigations. Energy on Mars is presented afterwards as a representative ISRU(In Situ Resource Utilization)-type energy resource, and we select three potential resources on Mars worth exploitation: solar energy, geothermal energy and wind energy. A model describing the global solar irradiance on Mars is concluded, typical applications of geothermal energy is analyzed, the phase equilibrium of geothermal fluids is established and the wind turbine is designed. Furthermore, the review on energy on Moon is started with the discussion on lunar geology relevant with energy resources, and an example of feature detection using Convolutional Neural Networks is illustrated as an example to demonstrate the application of deep learning techniques in space energy exploitation. Solar energy is always taken into account in space activities, and we are more focusing on the discussion of Helium-3, a promising resource for nuclear fusion. The material for nuclear fission, Uranium, has also been detected on Moon. A summary is provided in the end with concluding remarks. •A comprehensive review on space energy, with a thorough investigation on literature and international news.•Declaration of three main space energy utilization manners and information provided on the representative resources.•Study on the application of well-developed conventional energy development technologies on space energy utilizations.•Technic details on resource recognition, exploitation facilities and mechanism analysis.