With increasing interest to reduce the dependency on gasoline and diesel, alternative energy source like compressed natural gas (CNG) is a viable option for internal combustion engines. Spark-ignited (SI) CNG engine is the simplest way to utilize CNG in engines, but direct injection (DI) Diesel-CNG dual-fuel engine is known to offer improvement in combustion efficiency and reduction in exhaust gases. Dual-fuel engine has characteristics similar to both SI engine and diesel engine which makes the combustion process more complex. This paper reports the computational fluid dynamics simulation of both DI dual-fuel compression ignition (CI) and SI CNG engines. In diesel-CNG dual-fuel engine simulations and comparison to experiments, attention was on ignition delay, transition from auto-ignition to flame propagation and heat released from the combustion of diesel and gaseous fuel, as well as relevant pollutants emissions. Injection timing for diesel pilot was changed in a test matrix and the most efficient and least pollutant producing cases were selected and simulation results were correlated to the experimental data for those cases. The possible end-gas auto-ignition-like processes under certain test conditions like PREmixed Mixture Ignition in the End-gas Region (PREMIER) were also demonstrated. SI CNG lean burn engine tests and simulations were directed to check the ignitability, combustion stability, heat release rate for different spark energy values. The results show that a combined approach of using both chemical kinetics and G-equation formulations in RANS is capable of capturing most of the physical-chemical processes in both the dual-fuel CI and SI engine combustions.