Fish passage structures are constructed to facilitate fish moving to suitable habitats that are important during specific life stages. However, whether fish can successfully pass through a passage structure depends on their ability to swim against velocity barriers within the structure. Therefore, quantifying fish swimming ability is essential and to date, this knowledge is lacking for many species. Up to now, there is no widely-accepted method available to determine fish's ability crossing through velocity barriers. Establishment of such methods is important in both theoretical research and practical application. This review first summarized the widely-adopted methods for testing fish swimming ability. Swimming ability is mainly characterized by sustained swimming speed (i.e. the speed a fish can maintained for at least 200 minutes), critical swimming speed (i.e. the speed a fish can reach when using a step-wise protocol of speed increase) and burst speed (i.e. the maximum speed a fish can swim at, and this is usually maintained for <20 seconds). Critical swimming speed is the most common indicator of fish swimming ability. The critical swimming speed, burst speed and sustained speed are often used as references to design the fish passage, together with velocity field that is calculated by mathematical model. However, there are strong arguments that it is not effective to design fish passages according to the above swimming speeds because they are mainly determined in uniform flow condition which is significantly different from the complicated water flows in real passage structures. Unsteady flow (e.g. turbulence), which is a common phenomenon caused by the frictional effects of substrate and other objects in the water that disrupt laminar flow, might bring differences from laboratory results to field application. Thus, this review analyzed the key factors which affect fish crossing past velocity barriers, including fish behavior, metabolism, and hydraulics. Fish behavior has important influence on the ability to cross flow barriers, and such behaviors include sprinting, burst-glide, substratum skimming, jumping and flow refuging. Accordingly, researchers have defined the sprinting speed, gait transition speed, burst-glide speed and leaping ability of fishes to quantify their ability cross velocity barriers. Aerobic and anaerobic metabolism provides energy for fish swimming, and the related parameters such as oxygen consumption rate, blood glucose and lactate are effective indicators of a fish's ability to cross passage structures. In recent research, excessive post-exercise oxygen consumption and transport costs are used to measure energy expenditure during and after swimming in order to understand energy utilization and recovery. Hydraulics is another factor affecting fishes' ability to cross velocity barriers. It is observed that turbulence and jet-flows affect fish behavior and metabolism, thus affect passage success. Appropriate flow fields can increase the potential for fish to cross vertical slot fishways and culverts. In summary, a fish's ability to pass through velocity barriers is complicated and depends on several biotic and abiotic factors. Future studies are suggested to (1) analyze the relationships between swimming behavior, swimming ability and hydraulic condition, and (2) quantify the energy cost-recovery rate during fish crossing velocity barriers, and (3) develop mathematical models to describe the probability that a fish can pass through velocity barriers according to the above relationships between hydraulic condition, swimming behavior and energy dynamics.