Abstract Cutoffs, which include neck and chute cutoffs, are the results of the fluvial processes that fundamentally influence evolution of meandering rivers. A neck cutoff happens when the two limbs of a highly sinuous bend touch, whereas a chute cutoff refers to the formation of a shortcut channel passing through a meander bend. In this review, we begin by distinguishing the morphological and hydrological conditions of the two cutoff types. Mechanisms driving the development of a neck cutoff are embodied in a variety of kinematical and hydrodynamic models simulating processes governing the long-term evolution of meandering rivers. These models adopt a morphological threshold for judging the occurrence of a neck cutoff, b = αw , where α is a constant ranging between 0 and 1, b is the bend neck width and w is the mean channel width. The potential underestimation of the evolutionary period during the late stage of bend evolution toward a neck cutoff when using this morphological threshold and the uncertainties in quantifying the migration–curvature relationship limit the abilities of existing models to predict the occurrence of neck cutoffs. We then suggest three possible directions for future research on meander neck cutoffs. Mechanisms controlling chute cutoffs are relevant to six key factors representing the meander hydrological regime, planform morphology, bed topography and floodplain characteristics. The combination of these factors gives rise to four distinguishable triggering mechanisms: headward-erosion, embayment, mid-channel bar and scroll–slough chute cutoffs, though the initiation of the chute cutoff may be caused by some combination of these. However, the hydraulic and morphological characteristics of meander bends under these triggering mechanisms are so complex that they are often site-specific, making it extremely challenging to generalize the known morphodynamic and hydrodynamic processes driving the formation of chute cutoffs in individual meander bends. We close the review by recommending three possible research directions on chute cutoffs for tackling the existing challenges in the future.