Two-Phase Loops with Capillary Pump (Loop Heat Pipes (LHP) and Capillary Pumped Loops (CPL)) are currently among advanced thermal control technologies for aerospace applications. Large numbers of experimental and operational two-phase loops were successfully tested and used in several spacecraft in the past two decades. Novel technologies such as Advanced CPL-LHP, High Performance CPL, miniature LHPs, inversion (reversible, “Push-Pull") LHPs, ramified, multiple evaporator and condenser LHPs and CPLs, for complex thermal control systems are being proposed. This paper presents a state-of-the-art survey and analysis of these technologies. A classification of Two-Phase Loop with Capillary Pump designs is recommended. Basic principles, operational conditions and characteristics, temperature control and start-up initiation are discussed. The use of thermal control systems based on Two-Phase Loops with Capillary Pump for space applications is reviewed and summarized. The current and future trends of the technology for the aerospace sector are also discussed.