A process for digesting solid waste material comprises collecting the waste from a first location and transporting it to a second location where a fluids digestion vessel is located. At least some of the fluid fraction from the fluids digestion vessel is fed to the solids digestion vessel so that anaerobic digestion of the solid waste occurs in the solids digestion vessel. At least some of the digested solids waste is recovered, and the solids digestion vessel is preferably returned whence it came. The invention also provides apparatus for use in process.