Extensive analysis of the physical and chemical effects controlling the operation of combustion modes driven by auto-ignition is presented in this thesis. Specifically, the study integrates knowledge attained by analyzing the effects of fuel molecular structure on auto-ignition, quantity or quality of charge dilution, and in-cylinder temperature and pressure on burning characteristics in single and multiple injection strategies employed in compression ignition (CI), partially premixed combustion (PPC) and homogenous charge compression ignition (HCCI) engines. In the first section of the thesis, a multiple injection strategy aimed to produce heat at a constant pressure, commonly known as isobaric combustion, has been studied. Then, to eliminate the complexity of spray-to-spray interactions observed with isobaric combustion, the second section of the thesis is focused on compression ignition (CI) through single injection. In the final section, the presentation will move towards moderate conditions with high dilution, in which combustion becomes dominated by chemical kinetics. At these conditions, there is emerging evidence that certain fuels exhibit unusual heat release characteristics where fuel releases heat in three distinctive stages. Overall, the thesis discusses factors controlling the auto-ignition for CI, PPC and HCCI engines that can provide valuable insights to improve their operation. Isobaric combustion in CI engine involves large interactions between physical and chemical effects. Injection of spray jets into oxygen-deprived regions catalyzes the mechanism for soot production – urging to employ either multiple injectors, low reactivity fuel or an additional expansion stage. Fuels – regardless of their auto-ignition tendency – share the same combustion characteristics in the high load CI, where auto-ignition is controlled by only the injector’s physical specifications. Such observation is a showcase of the fuel flexible engines that has the potential of using sustainable fuels – without being restrained by the auto-ignition properties of the fuel. The thesis provides evidence from experiment and simulation that three-stage auto-ignition is indeed a phenomenon driven by chemical kinetics. Three-stage auto-ignition opens the perspective to overcome the limitation of the high-pressure rise rates associated with HCCI engine.