With the rapid development of human space technology, space photography is increasingly being applied to tasks such as satellite observation, debris collection, and deep-space exploration. However, extreme space environments and inherent deviations of imaging systems may lead to the accumulation of degradations, not only results in low-quality imaging results, but also hampers the performance of downstream applications such as object detection, tracking, and attitude estimation. Under extreme space imaging conditions, we focus on four key image enhancement tasks, including image denoising, deblurring, super-resolution and multi-exposure image fusion. We review the classic and deep learning-based methods, summarize the characteristics and analyze the practical problems in the space imaging process. The paper also presents timelines of method development and lists databases for training, validating and testing, providing a comprehensive overview and a reference for research on extreme space image enhancement. Furthermore, we discuss critical directions that need to be addressed in the future to advance new technologies for high-resolution imaging in extreme space environments.