Anaerobic digestion (AD) for waste, and wastewater, management was identified in the 1970s as a forerunner in the push for sustainability. The development of AD applications resulted in the discovery of "anaerobic granules," which are multitrophic bio-aggregates comprising methanogenic consortia capable of digesting waste organics to methane-rich biogas suitable for use as a renewable bioenergy. In the intervening years the emergence of the anaerobic ammonium oxidizing (anammox) granule, aerobic granule, hydrogenic granule, oxygenic photogranule, and many other functionally-specialized granules, has opened new opportunities in wastewater treatment, and resource-recovery, biotechnology. As a single entity, a granule represents an entire community of microorganisms. This review compares three of the most influential types: the anaerobic (methanogenic), aerobic and anammox granule. The main characteristics, biochemical processes, and typical makeup of the microbial community in each type are discussed. Finally, the adoption of granules as an intriguing "playground" for experiments in microbial ecology is reviewed.