Anaerobic digestion (AD) is an attractive and sustainable alternative for stabilizing solid organic waste and producing biogas or biomethane. However, it is carried out by slow-growing bacteria and archaea and it normally demands a hydraulic retention time (HRT) of 20-60 days in the bioreactor. Although high-rate AD methods and technologies have been developed, they are normally applied to liquid wastes such as wastewater. In this work, the theory and latest developments in high-rate digestion of organic solid wastes are reviewed. The process is accomplished by running the AD in a two-stage operation. The first stage involves dissolving the solid materials in water, using robust hydrolytic bacteria. The effluent is then filtered to remove any undigested material, which in some cases contains inhibitory compounds. The filtrate is then fed to bioreactors containing high cell density ADs such as flocculating bacteria (granules) or membrane bioreactors (MBR) to protect the sensitive and very slow-growing methanogen. Different approaches to overcoming problems faced in the first stage of digestion are proposed in this review. These problems include slow digestion of lignocellulosic biomass or failure of digestion due to inhibition problems for feedstocks containing toxic compounds, and rapid acidification for easily degradable substrates. The principle, technology, benefits and drawbacks, and factors affecting the efficacy of each type of high cell-density reactor are presented. (c) 2019 Society of Chemical Industry and John Wiley & Sons, Ltd.