Anaerobic digestion (AD) processes can face operational challenges or flaws such as substrate structure and characteristics complexity, process complexity, low productivity, inefficient biodegradability, and poor stability, which suppresses or reduces biogas and biomethane production. As a result of the need to overcome these challenges/shortcomings and improve or enhance biogas and biomethane yield, process intensification methods have gained attention. There is some literature review on pretreatment and co-digestion as a means of improving AD performance; however, there is no systematic information on the various strategies required for improving AD performance and, in turn, increasing biogas/biomethane yield. The AD process produces biogas, a valuable renewable biofuel. Biogas is composed primarily of biomethane and other undesirable components such as carbon dioxide, oxygen, hydrogen sulphide, water vapour, ammonia, siloxanes, nitrogen, hydrocarbons, and carbon monoxide, which act as impurities or contaminants and tend to reduce the biogas specific calorific value while also causing various problems with machine operation. As a result, various technologies are used to improve raw biogas quality by removing contaminants during biogas transformation to biomethane. As a result, this paper provides a comprehensive review of the various systematic process intensification strategies used to overcome AD process challenges/shortfalls, improve or enhance biogas and biomethane production, and conventional and emerging or advanced technologies for biogas purification, cleaning, and upgrading.