The continual generation and discharge of waste are currently considered two of the main environmental problems worldwide. There are several waste management options that can be applied, though anaerobic digestion (AD) process technology seems to be one of the best, most reliable, and feasible technological options that have attracted remarkable attention due to its benefits, including the generation of renewable energy in the form of biogas and biomethane. There is a large amount of literature available on AD; however, with the continuous, progressive, and innovative technological development and implementation, as well as the inclusion of increasingly complex systems, it is necessary to update current knowledge on AD process technologies, process variables and their role on AD performance, and the kinetic models that are most commonly used to describe the process-reaction kinetics. This paper, therefore, reviewed the AD process technologies for treating or processing organic biomass waste with regard to its classification, the mechanisms involved in the process, process variables that affect the performance, and the process kinetics. Gazing into the future, research studies on reduced MS-AD operational cost, integrated or hybrid AD-biorefinery technology, integrated or hybrid AD-thermochemical process, novel thermochemical reactor development, nutrient recovery from integrated AD-thermochemical process, and solid and liquid residual disposal techniques are more likely to receive increased attention for AD process technology of biomass wastes.