With benefits to the human health, environment, economy, and energy, anaerobic digestion (AD) systems have attracted remarkable attention within the scientific community. Anaerobic digestion system is created from (bio)reactors to perform a series of bi-metabolism steps including hydrolysis/acidogenesis, acetogenesis, and methanogenesis. By considering the physical separation of the digestion steps above, AD systems can be classified into single-stage (all digestion steps in one reactor) and multi-stage (digestion steps in various reactors). Operation of the AD systems does not only depend on the type of digestion system but also relies on the interaction among growth factors (temperature, pH, and nutrients), the type of reactor, and operating parameters (retention time, organic loading rate). However, these interactions were often reviewed inadequately for the single-stage digestion systems. Therefore, this paper aims to provide a comprehensive review of both single-stage and multi-stage systems as well as the influence of the growth factors, operating conditions, and the type of reactor on them. From those points, the advantages, disadvantages, and application range of each system are well understood.