Anaerobic processes for treatment of low and high strength wastewaters and solid wastes constitute the core method in the natural biological mineralization (NBM) treatment concept. When adequately combined with the complementary NBM-systems and modern clean water saving practices in wastewater collection and transport, they represent a feasible route to sustainable environmental protection (EPsus), in essence even towards a more sustainable society. Despite the development and implementation of modern high rate Anaerobic Wastewater Treatment (AnWT-) systems and complementary innovative NBM-processes, the considerable progress made since the seventies in fundamental insights in microbiology, biochemistry and process technology, still numerous challenging improvements in the NBM-field can be realized. This contribution is mainly based on the insights attained from wide ranging literature evaluations and the results of experimental research conducted by numerous PhD students who participated in our group over the last four decades. An attempt is made here to identify major facets on which an improved insight can, and consequently should, be obtained in order to accomplish more optimal operation and design of various types of Anaerobic Degradation (AnDeg-) processes.