Multiple autonomous underwater vehicles (MAUV) are increasingly applied to marine exploration and resource development. As such, they have been widely explored. In this paper, the tasks and methods of common MAUV are discussed, and the key problem of cooperation among MAUV is comprehensively investigated from the perspective of emerging functions. Firstly, the cooperation among MAUV is classified according to task-, motion-, and measurement-space aspects and their combination. Secondly, different kinds of MAUV and their realization methods are introduced from three perspectives. Lastly, the future research direction of MAUV is discussed. This survey is conducted to provide strategies and approaches for MAUV and help accomplish underwater tasks efficiently and cooperatively in complex ocean-related application scenarios.