Artificial Intelligence (AI) is increasingly finding acceptance in the space community, especially Machine Learning (ML), a subdomain of AI. ML algorithms now find numerous applications in autonomous navigation, spacecraft health monitoring and operational management of satellite constellations. However, a large number of surveys on the applications of AI in space missions can be classified into two categories. The first category suffers from the limitation of being old and not covering some crucial and recent developments in the field; such as the contributions of Deep Learning (DL) and bioinspired AI algorithms. The challenge with the second category lies in its being too detailed with respect to the development and application of specific AI techniques or algorithms. These limitations have necessitated the need to have a concise survey with a wider scope for those interested in the applications and challenges of AI in the space industry, especially those with technical backgrounds in other fields. In this paper, we surveyed the use of traditional AI techniques in various domains of space missions without delving into formal methods. Some bioinspired AI algorithms were also surveyed and their potential application areas highlighted. Unlike similar surveys that focus only on technological challenges, we also addressed some crucial legal drawbacks that emanate from the reliance and use of AI in space. Summarily, while discussing future directions we reviewed some advancements in Internet of Things (IoT) and Blockchain technologies. Our review prioritized three application domains positioned to benefit immensely from the inevitable AI-Blockchain convergence in the space community. These include the Internet of Space Things (IoST), Satellite Communication and Spacecraft Data Security.