The overall goal of this work is to understand non-ideal effects in practical rotating detonation engines (RDEs) that impede the realization of theoretical detonation cycle efficiencies. The main limitations in RDE operability and performance are associated with practical design considerations, where non-idealities, such as incomplete mixing, fuel leakage, secondary deflagration, instabilities and geometry-dependent effects, reduce the effectiveness of the detonation-based compression cycle. The goal of this work is to take a fundamental point of view, and use detailed experiments and simulations to understand non-ideal effects, their contribution to loss in pressure gain, and RDE operability limitations. Current research is mainly focused on design and overall operability of RDEs. Our approach is instead to look at the physics of basic processes occurring in RDEs. In particular, we consider processes associated with non-idealities and we use a combination of laser and non-laser diagnostics and large eddy simulation/direct numerical simulation computations to investigate these underlying phenomena. By advancing the fundamental science of detonation wave propagation in RDE flowfields, and subject to non-ideal conditions, will enable design to progress more rapidly. This work is a collaborative work involving experiments, simulations and external domain experts to understand the physics behind RDEs and non-idealities. Through collaboration between experimentalists and modelers, we have developed targeted experiments to investigate fundamental aspects of the operation of an RDE. Furthermore, we have developed advanced combustion models that account for non-ideal effects in the operation of an RDE and are able to capture the complexities of realistic RDE configurations. We conduct detailed physical and computational experiments to investigate the flame structure ahead and behind detonation fronts in the presence of non-uniform or incomplete mixing, leakage and secondary combustion. We use optical and laser diagnostics to identify the structure of the detonation wave. We consider different working parameters, such injection scheme, geometry, flow rates and equivalence ratios. We brought in DNS/LES capabilities to RDE design by specifically incorporating detailed kinetics and pressure-sensitive combustion physics, thus improving upon current practice based on an Euler equations description that do not take into account viscous effects, while the combustion process is introduced using an induction time based global ignition model. These current models lack the capability of capturing non-ideal mixing and fuel stratification effects ? limitations that models and analysis developed in this work have been reduced. Furthermore, the significant changes in pressure within the domain due to the detonation requires combustion models with time-varying pressure effects. In this regard, using DNS with detailed chemistry, and developing LES-based combustion models for complex geometries with detonation wave has enable to understand some of the underlying phenomena controlling the operation of these devices. The main objectives developed by the project are the following ones: Objective 1. Develop canonical and operational RDE configurations, as well as imaging-based diagnostics for understanding fuel stratification, leakage, deflagration and detonation structure under non-ideal conditions in RDEs. Objective 2. Develop detailed computational tools for studying detonation wave propagation processes in RDEs. Objective 3. Develop a comprehensive picture of the fundamental physics governing non-idealities and how they impact RDE performance and operability from both experiments and simulations.