Most morphodynamic models of river meandering assume spatially constant width; depending on the intensity of spatial width variations, different meandering styles actually exist, often associated with midchannel bars and islands. When intense enough, width oscillations characterize transitional planforms between meandering and braiding. We investigate, on a modeling basis, morphodynamic feedbacks between spatial curvature and width oscillations in river meanders and related bedform patterns. Our review of existing mathematical models suggests that width-curvature interactions can be comprehensively analyzed by a hierarchy of models that descend from a two-parameter perturbation solution of the governing depth-averaged morphodynamic model. The focus is on in-stream, autogenic hydromorphodynamic processes, and not explicitly on bank processes. Curvature-width interactions are fundamentally nonlinear: the perturbation approach allows us to investigate the key effects at the first nonlinear interaction. In meanders with initially constant width, curvature nonlinearly forces midchannel bar growth, promoting symmetrical bank erosion further downstream, possibly triggering width oscillations. These in turn can significantly affect the process of bend stability and therefore condition the curvature dynamics. Wider-at-bends meanders develop shorter bends and are morphologically more active compared to equiwidth meanders, coherently with the few available field observations. River evolution models aiming to separately simulate bank erosion and accretion processes should incorporate these autogenic flow-bed nonlinearities. Because of its focus on meandering morphologies close to the transition with braiding, the proposed approach can be taken as a novel, physically based viewpoint to the long-debated subject of channel pattern selection.