Plastic waste is an issue of global concern because of the environmental impact of its accumulation in waste management systems and ecosystems. Biodegradability was proposed as a solution to overcome this problem; however, most biodegradable plastics were designed to degrade under aerobic conditions, ideally fulfilled in a composting plant. These new plastics could arrive to anaerobic environments, purposely or frequently, because of their mismanagement at the end of their useful life. This review analyzes the behavior of biodegradable and conventional plastics under anaerobic conditions, specifically in anaerobic digestion systems and landfills. A review was performed in order to identify: (a) the environmental conditions found in anaerobic digestion processes and landfills, as well as the mechanisms for degradation in those environments; (b) the experimental methods used for the assessment of biodegradation in anaerobic conditions; and (c) the extent of the biodegradation process for different plastics. Results show a remarkable variability of the biodegradation rate depending on the type of plastic and experimental conditions, with clearly better performance in anaerobic digestion systems, where temperature, water content, and inoculum are strictly controlled. The majority of the studied plastics showed that thermophilic conditions increase degradation. It should not be assumed that plastics designed to be degraded aerobically will biodegrade under anaerobic conditions, and an exact match must be done between the specific plastics and the end of life options that they will face.