A paradigm shift in how mankind investigates and functions outside of Earth’s borders is represented by the incorporation of agentic artificial intelligence in space travel. The revolutionary significance of autonomous AI systems in space missions is examined in this chapter, with particular attention to the systems’ ability to make decisions on their own in harsh conditions. We provide a thorough examination of the various applications of AI in space exploration that are now in use, such as adaptive mission planning, real-time resource management, and autonomous navigation systems. We show how agentic AI systems may optimise spaceship operations, lower mission risks, and enable hitherto unheard-of levels of exploration efficiency through mathematical modelling and experimental validation. In order to improve decision-making, our work presents new frameworks for multi-agent cooperation in space contexts that include quantum computing components. The usefulness and advantages of agentic AI systems are demonstrated through case studies of recent Mars missions and deep-space exploration projects. The chapter also looks at new developments in space-based AI, such as AI-driven space habitat management, swarm intelligence for asteroid mining, and self-repairing systems. According to our research, agentic AI will play a key role in allowing for a sustainable human presence outside of Earth, which will have an impact on resource use and interplanetary colonisation.