Machine learning, particularly deep learning, is being increasing utilised in space applications, mirroring the groundbreaking success in many earthbound problems. Deploying a space device, e.g. a satellite, is becoming more accessible to small actors due to the development of modular satellites and commercial space launches, which fuels further growth of this area. Deep learning's ability to deliver sophisticated computational intelligence makes it an attractive option to facilitate various tasks on space devices and reduce operational costs. In this work, we identify deep learning in space as one of development directions for mobile and embedded machine learning. We collate various applications of machine learning to space data, such as satellite imaging, and describe how on-device deep learning can meaningfully improve the operation of a spacecraft, such as by reducing communication costs or facilitating navigation. We detail and contextualise compute platform of satellites and draw parallels with embedded systems and current research in deep learning for resource-constrained environments.