The present invention relates to an anaerobic reactor (10) for the treatment of industrial and other wastewaters at psychrophilic temperatures, the reactor comprising a mixing chamber (12) in which is located, during use, a granular sludge fluidized bed, the reactor further comprising a biofilm chamber (16) fed from the mixing chamber and housing a biofilm colonized pumice-based carrier material, and a separation chamber (18) in fluid communication with the biofilm chamber and in which treated effluent and biogas produced within the reactor are separated.