Pipes are widely employed in marine, nuclear power, aerospace and other important engineering applications. The pipe is one of the most key structures for engineering equipment such as the oil production platform and the steam generator. When the external fluid flows through the pipe, fluidstructure interaction vibration behavior of the pipe occurs, leading to vibration damage and fatigue failure of the engineering equipment. It has become a key problem that must be solved in engineering design. As to the scientific issues on nonlinear dynamical mechanism for fluidstructure interaction vibrations of flexible pipes subjected to external flows, this paper reviews the important research progress over the world scholars, focusing on discussing the nonlinear fluidstructure interaction vibrations of flexible pipes subjected to external cross flows and axial flows, respectively. The influence mechanism of external flows on dynamic behaviors of the pipe is revealed from aspects of the experimental research, computational fluid dynamics simulation and theoretical modeling. Finally, the current research status is briefly summarized and the research difficulties and challenges still exist in this field are proposed.