Low cost, efficient two-stage anaerobic digestion systems for the production of biogas (e.g. methane) are provided. During the first stage, biogas is produced in a first reactor by anaerobic microbes cultured in two phases: a high solids phase and a low solids phase. During the second stage, biogas is produced in a second reactor by a methanogen-rich anaerobic culture cultured in low solids medium. Removal of effluent comprising pH lowering reaction products assists in maintaining a suitable pH in the high solids phase. The transfer of effluent from the second reactor to the first reactor assists in maintaining a suitable pH in the high solids phase, in mixing of the high solids phase, and in reseeding the high solids phase with methanogens. Methane is produced in and recovered from both reactors.