This thesis aims to contribute to the research and development of a new highly efficient split-cycle engine concept – the double compression-expansion engine (DCEE) – by expanding the knowledge of combustion processes suitable for this and, potentially, other modern engines, via experimental and computational studies. In this work, first, the importance of continued improvement of internal combustion engines is demonstrated by comparing the life-cycle CO2 emissions of different modes of transport, including walking and bicycling. Then, an isobaric combustion concept is proposed for use in modern high-pressure combustion engines, such as the DCEE. Isobaric combustion is compared to conventional diesel combustion at different pressure levels, fueling, and EGR rates, and shown to reduce cylinder wall heat transfer losses by 20 %, simultaneously improving the NOx emissions by a factor of two. An in-situ injection rate measurement technique is developed and applied to improve the understanding of the complex injection strategies required for isobaric combustion. It is also shown that isobaric combustion is possible to achieve with a single fuel injector, but using multiple injectors may offer additional benefits of even lower heat losses, better heat release control, and improved soot and NOx trade-off. Then, an alternative combustion system to the diesel isobaric is proposed – a hydrogen direct-injection (DI) compression-ignition (CI) combustion concept, which has the advantage of ideally eliminated CO2 and soot emissions. DICI H2 combustion is found to differ significantly from conventional diesel, most importantly, in terms of the injected and retained momentum, and in-cylinder flow patterns and fuel-air mixing. Thus, a completely different optimization path must be taken for H2 engines, which involves maximizing the free-jet mixing phase of combustion while minimizing the momentum-dominated global mixing phase. This is achieved computationally in this work by adapting the combustion chamber shape to the H2 jets and modifying the injector nozzle, which proved effective. Finally, hydrogen combustion is computationally compared to diesel in the context of the DCEE on the basis of thermodynamic system parameters and detailed energy breakdown, and proved superior. Brake thermal efficiencies in the range of 56 % are demonstrated for the entire DCEE powertrain fueled with hydrogen.