Anaerobic digestion (AD) serves as a promising alternative for waste treatment and a potential solution to improve the energy supply security. The feasibility of AD has been proven in some of the technologically and agriculturally advanced countries. However, development is still needed for worldwide implementation, especially for AD process dealing with municipal solid waste (MSW). This paper reviews various approaches and stages in the AD of MSW, which used to optimise the biogas production and quality. The assessed stages include pre-treatment, digestion process, post-treatment as well as the waste collection and transportation. The latest approaches and integrated system to improve the AD process are also presented. The stages were assessed in a relatively quantitative manner. The range of energy requirement, carbon emission footprint and the percentage of enhancement are summarised. Thermal hydrolysis pre-treatment is identified to be less suitable for MSW (−5% to +15.4% enhancement), unless conducted in the two-phase AD system. Microwave pre-treatment shows consistent performance in elevating the biogas production of MSW, but the energy consumption (114.24–8,040 kWeh t−1) and carbon emission footprint (59.93–4,217.78 kg CO2 t−1 waste) are relatively high. Chemical (∼0.43 kWeh m−3) and membrane-based (∼0.45 kWeh m−3) post-treatments are suggested to be a lower energy consumption approach for upgrading the biogas. The feasibility in terms of cost (scale up) and other environmental impacts (non-CO2 footprint) needs to be further assessed. This study provides an overview to facilitate further development and extended implementation of AD.