There has been intense debate over the depletion of fossil fuel reserves in recent decades as well as the greenhouse gas emissions that are causing climate change. At the same time, new legislation in Greece, national policies, European policies, and realistic needs, need effective waste management and the protection of national resources. As a result, it seems a necessity to exploit waste treatments, while expanding the use of renewable energy sources. In this study, an attempt is made to focus our interest and research on a specific biomass waste stream, namely the waste biomass from the agricultural-livestock sector. The possibility of processing these wastes through the technology of biomass biorefinery with anaerobic digestion as its central process will be studied. The technology of anaerobic digestion is a process widely used for the treatment of agricultural residues and livestock waste as well as for the exploitation of energy crops (energy development, soil enhancement) mainly in countries in Europe and globally. This study reviews the biorefinery biomass technology, the energy production technology, production of biofuels, and new materials from waste biomass at the behest of the circular economy and bioeconomy. Additionally, this research will be an introduction in maximizing the potential of the full utilization of agricultural and livestock waste, and the by-products that can be produced from these processes.