Attention to the microwave design of waveguide photodetectors leads to travelling-wave photodetectors. These devices show bandwidths as high as 172 GHz, the highest reported for a p-i-n photodetector, and bandwidth efficiency products as large as 76 GHz, the largest reported for any photodetector without gain. Direct comparisons with vertically illuminated and waveguide photodetectors confirm the advantages of travelling-wave photodetectors.< >