As the impacts of global warming have become increasingly severe, oxy-fuel combustion has been widely considered a promising solution for carbon capture and storage (CCS) to reduce carbon dioxide (CO2) to achieve net-zero emissions. In the past few decades, researchers around the world have demonstrated improvements by the application of oxy-fuel combustion to internal combustion (IC) engines. This article presents a comprehensive review of the experimental and simulation studies about oxy-combustion for CCS in IC engines. To give a more comprehensive understanding, it has included a detailed explanation of the essential components contained in an oxy-fuel IC engine and its typical operating parameters. The oxy-fuel IC engine components include the system of oxygen supply, exhaust gas recirculation (EGR), water injection, fuel injection, and CCS. In order to optimise the combustion process, it is required to adopt the appropriate values for the oxygen concentration, EGR rate, ignition timing, compression ratio, fuel injection, and water injection in oxy-fuel engines. The detailed literature review and analysis presented provide a basis for the selection of oxy-fuel combustion for CCS as a prospective solution to reduce carbon emissions in IC engines.