In this Perspective, we explore the instability of a meandering channel with variable width and curvature. The analysis employs the depth-averaged formulations for the flow and sediment transport. Unlike the conventional instability analysis that considers mainly the bedload transport, we consider the generic sediment transport including both the bedload and suspended load. The analysis addresses the variations of the near-bank excess azimuthal velocity and the bed topography deviation with the meander wavenumber for different pertinent parameters, such as Shields number, relative roughness number, channel aspect ratio, width-variation amplitude, and shear Reynolds number. The analysis detects a resonance phenomenon for certain critical values of the pertinent parameters and explores the sensitivity of the resonant wavenumber to the pertinent parameters. In a hydraulically smooth flow regime, the sediment suspension is found to play a stabilizing role. On the contrary, in hydraulically transitional and rough flow regimes, the sediment suspension offers a destabilizing effect. The stability diagrams reveal that the stable zone enlarges as the Shields number and relative roughness number increase, while it contracts with an increase in width-variation amplitude. For a given shear Reynolds number in a hydraulically smooth flow regime, the stability diagram predicts various stable zones. By contrast, for a given shear Reynolds number in hydraulically transitional and rough flow regimes, a unique stable zone exists. © 2021 Author(s).