The velocity-matched distributed photodetectors (VMDP) with high saturation power and large bandwidth have been proposed and demonstrated. The theoretical analysis on the trade-off between saturation power and bandwidth shows that VMDP provides fundamental advantages over conventional photodetectors. The theory for designing and simulating the performance of the VMDP is developed comprehensively from the aspect of microwave transmission line, optical waveguide, and the VMDP structure. The VMDP with very high saturation photocurrent (56 mA) and instrument-limited bandwidth (49 GHz) is demonstrated experimentally. The theoretical analysis and experimental results show that VMDP is attractive for high-performance microwave photonics links and high-power optical microwave applications.