Biogas is commonly produced during the decay of organic matter. It is a mixture of methane and some non-combustible gases such as CO2 and H2S. Its viability as a renewable alternative fuel for internal combustion engines can be enhanced by methane enrichment, i.e. removal of the non-combustible constituents. One of the common techniques for using biogas in a compression ignition (CI) engine is to mix it with air in the intake manifold, induct, and compress this mixture and ignite it by injecting a small quantity of diesel or bio-diesel, which is termed as the pilot fuel. This is known as the dual fuel mode. The pilot fuel is injected close to the end of the compression stroke as in a conventional CI engine and the injected fuel quantity depends on the operating condition. An alternative approach is the Homogeneous Charged Compression Ignition (HCCI) mode. Here, a homogeneous mixture of biogas and air is inducted and compressed by the piston until it auto-ignites. While this concept combines the benefits of spark ignition (SI) and CI engines, the onset of combustion cannot be controlled directly. A detailed review of recent research pertaining to biogas purification techniques and operation of CI engines with biogas in dual fuel and HCCI modes is presented in this paper. The effects of various operating parameters on engine performance and emissions, and comparison with conventional diesel fuelled CI engines are discussed. Biogas improves combustion efficiency, NOx, and smoke emissions. However, it reduces brake thermal efficiency, volumetric efficiency, and increases HC and CO emissions. Biogas fuelling of CI engines is recommended for achieving high diesel substitution, especially under high torque operation.