Flood routing is an important topic in engineering hydrology and an integral part of flood management and hydrodynamic modelling studies. Muskingum and Muskingum-Cunge methods are commonly used in flood routing studies. Here, we perform a systematic review of research on linear and non-linear Muskingum and Muskingum-Cunge flood routing methods to document how they have contributed to the development of flood science. Specifically, we document the evolution of publications involving Muskingum flood routing methods between 1938 and 2021. Research gaps progressively filled over time include the use of optimization algorithms, and tools for uncertainty and sensitivity analysis. In addition, we document various case studies that were conducted to improve flood routing performance. The chronological analysis reveals performance improvement of Muskingum and Muskingum-Cunge models in terms of cost effectiveness, user friendliness and ease of use.
