In spite of the excellent capabilities of machine learning algorithms, their performance deteriorates when the distribution of test data differs from the distribution of training data. In medical data research, this problem is exacerbated by its connection to human health, expensive equipment, and meticulous setups. Consequently, achieving domain generalizations (DG) and domain adaptations (DA) under distribution shifts is an essential step in the analysis of medical data. As the first systematic review of DG and DA on functional brain signals, the paper discusses and categorizes various methods, tasks, and datasets in this field. Moreover, it discusses relevant directions for future research.