Remediation of organic dyes in natural waters is a significant environmental need under active study. This review analyzes bimetallic catalytic degradation systems that are based on the Fenton chemistry concept and that generate reactive oxygen species (ROS) as the agent of dye breakdown. Recently developed advanced oxidation processes (AOPs) take advantage of bimetallic heterogeneous catalysts to facilitate rapid rates and full degradation. Catalysts based on two metals including iron, copper, molybdenum, cobalt and magnesium are discussed mechanistically as examples of effective radical ROS producers. The reactive oxygen species hydroxyl radical, superoxide radical, sulfate radical and singlet oxygen are discussed. System conditions for the best degradation are compared, with implementation techniques mentioned. The outlook for further studies of dye degradation is presented.