Because of their wide detection range and rich functions, autonomous underwater vehicles (AUVs) are widely used for observing the marine environment, for exploring natural resources, for security and defense purposes, and in many other fields of interest. Compared with a single AUV, a multi-AUV formation can better perform various tasks and adapt to complex underwater environments. With changes in the mission or environment, a change in the UAV formation may also be required. In the last decade, much progress has been made in the transformation of multi-AUV formations. In this paper, we aim to analyze the core concepts of multi-AUV formation transformation; summarize the effects of the AUV model, underwater environment, and communication between AUVs within formations on formation transformation; and elaborate on basic theories and implementation approaches for multi-AUV formation transformation. Moreover, this overview includes a bibliometric analysis of the related literature from multiple perspectives. Finally, some challenging issues and future research directions for multi-AUV formation transformation are highlighted.