Improved methods for anaerobic digestion of organic matter to produce biogas. Among the improvements given are including ferric iron in a hydrolysis reactor to increase the rate and efficiency of anaerobic hydrolysis to provide substrates for methanogenesis. A solids separation step is added after hydrolysis and before methanogenesis to improve the efficiency of the methanogenesis step. Other improvements involve using separate tanks for the hydrolysis and methanogenesis stages and using two (or more) methanogenesis tanks in sequence, and switching the order of the two (or more) methanogenesis tanks periodically.