Anaerobic digestion (AD) is a process in which microorganisms, under oxygen-free conditions, convert organic matter into biogas and digestate. Normally, only 40–70% of biomass is converted into biogas; therefore, digestate still contains significant amounts of degradable organic matter and biogas potential. The recovery of this residual biogas potential could optimize substrate utilization and lower methane emissions during digestate storage and handling. Post-treatment methods have been studied with the aim of enhancing the recovery of biogas from digestate. This review summarizes the studies in which these methods have been applied to agricultural and wastewater digestate and gives a detailed overview of the existing scientific knowledge in the field. The current studies have shown large variation in outcomes, which reflects differences in treatment conditions and digestate compositions. While studies involving biological post-treatment of digestate are still limited, mechanical methods have been relatively more explored. In some cases, they could increase methane yields of digestate; however, the extra gain in methane has often not covered treatment energy inputs. Thermal and chemical methods have been studied the most and have yielded some promising results. Despite all the research conducted in the area, several knowledge gaps still should be addressed. For a more thorough insight of the pros and cons within post-treatment, more research where the effects of the treatments are tested in continuous AD systems, along with detailed economic analysis, should be performed.