Aerobic sludge granules are suspended biofilms with the potential to reduce the cost and footprint of secondary wastewater treatment. Attempts to answer how and why they form leads to a consideration of the role of their extracellular polymeric substances (EPS) in determining their physical and microbiological properties. The exopolysaccharide components of this matrix, in particular, have received attention as putative structural, gel-forming agents. Two quite different exopolysaccharides have been proposed as the gel-forming constituents, with their gel properties clearly different from those of activated sludge EPS. This review aims to address the question of whether more than one gel-forming exopolysaccharide exist in granules. Based on the available structural data, it seems likely that they are different gel-forming polymers and their differences are not artifacts of the analytical methods used. Nonetheless, both proposed structural gel polymers are extracted and purified based on procedures selecting for anionic polar polysaccharides soluble at high pH, and both contain hexuronic acids. Granulation does not result from EPS synthesis by any single microbial population, nor from production of a single exopolysaccharide. Future studies using solvents suitable for recalcitrant polysaccharides are likely to reveal important structural roles for other polysaccharides. It is hoped that this article will serve as a guide for subsequent studies into understanding the roles of exopolysaccharides in aerobic granular sludge.