We investigate the influence of vegetation on river morphological instabilities using an analytical framework. We first discuss the important role of the hydrological (flooding frequency) and biological (vegetation development rate) timescales. As long as the changes in riverbed morphology and vegetation over an interval comprising one flood and one low-flow period are small, we show that it is possible to simplify the description of a vegetated river with non-constant discharge. We propose physically-based and effective (neural) models for the feedback between vegetation and morphodynamics. Physically-based approaches use equations of morphodynamics extended to account for the interplay between flow, sediment and vegetation dynamics. While their foundation is solid, a physically-based description is only feasible for simple vegetation cover (grass to shrubs). For complex vegetated obstacles we present as an alternative effective approaches, explicitly including interactions (local and non-local) between obstacles. We focus on the role of vegetation in the emergence of ridge patterns observed in the presence of an ephemeral flow and correspondingly derive a set of conditions for patterns. (C) 2015 Elsevier Ltd. All rights reserved.