Abstract: A rotating detonation combustor includes an annular combustion passage that is non-circular. Specifically, the present rotating detonation combustor includes a forward wall, a radially inner wall, and a radially outer wall. The radially inner wall and the radially outer wall extend downstream from the forward wall around a longitudinal axis of the combustor, thus defining an annular passage between the radially inner wall and the radially outer wall. An air inlet and a fuel inlet are disposed proximate to the forward wall and in fluid communication with the annular passage. The cross-section of the annular passage, which can be elliptical or polygonal, is defined by arcuate and/or straight sides of the inner and outer walls.