Sediment traps with open check dams are widely used structures in flood hazard mitigation. This paper reviews the literature dedicated to their design. First, the general context in which sediment traps are built and their functions are presented. The second part proposes hydraulic design criteria for classical types with details on the opening shapes and dam crest spillway. The third part details sediment deposition dynamics: its initiation, its controls through the trap basin and open check dam shapes, the effect of hydrographs, and the control of trap self-cleaning. The methods to determine the deposit slope and height are discussed. Finally, a step-by-step design procedure is proposed and future research challenges are highlighted. Field feedback has shown that driftwood can substantially influence sediment trap behavior. A companion paper thoroughly covers the production and transfer of driftwood and the interactions with open check dams.