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The development and adoption of artificial intelligence (AI) technologies in space applications is growing quickly as the consensus increases on the potential benefits introduced. As more and more aerospace engineers are becoming aware of new trends in AI, traditional approaches are revisited to consider the applications of emerging AI technologies. Already at the time of writing, the scope of AI-related activities across academia, the aerospace industry and space agencies is so wide that an in-depth review would not fit in these pages. In this chapter we focus instead on two main emerging trends we believe capture the most relevant and exciting activities in the field: differentiable intelligence and on-board machine learning. Differentiable intelligence, in a nutshell, refers to works making extensive use of automatic differentiation frameworks to learn the parameters of machine learning or related models. Onboard machine learning considers the problem of moving inference, as well as learning, onboard. Within these fields, we discuss a few selected projects originating from the European Space Agency's (ESA) Advanced Concepts Team (ACT), giving priority to advanced topics going beyond the transposition of established AI techniques and practices to the space domain.