Poor long-term stability of aerobic granules developed in sequencing batch reactors (SBRs) remains a limitation to widespread use of aerobic granulation in treating wastewater. Filamentous growth has been commonly reported in aerobic granular sludge SBR. This review attempts to address the instability problem of aerobic granular sludge SBR from the perspective of filamentous growth in the system. The possible causes of filamentous growth are identified, including long retention times of solids, low substrate concentration in the liquid phase, high substrate gradient within the granule, dissolved oxygen deficiency in the granule, nutrient deficiency inside granule, temperature shift and flow patterns. Because of cyclic operation of aerobic granular sludge SBR and peculiarities of aerobic granules, various stresses can be present simultaneously and can result in progressive development of filamentous growth in aerobic granular sludge SBR. Overgrowth of filamentous bacteria under stress conditions appears to be a major cause of instability of aerobic granular sludge SBR. Specific recommendations are made for controlling filamentous growth.