Many river restoration projects seek to address issues associated with impaired hydrological and ecological connectivity in longitudinal (e.g. effects of dams, weirs) or lateral (e.g. alienated floodplain) dimensions. Efforts to restore the vertical dimension of impaired stream–groundwater exchange are rare, hampered by limited understanding of the factors controlling this linkage in natural alluvial rivers. We propose a simplified two-axis model of the 'primary drivers' (sediment structure and vertical hydraulic gradient) of stream–groundwater exchange that acknowledges their interaction and provides a practical template to help researchers and river managers pose hypothesis-driven solutions to restoration of damaged or lost vertical connectivity. Many human activities impact on one or both of these drivers, and we review some of the tools available for treating the causes (rather than symptoms) in impacted stream reaches. For example, creating riffle-pool sequences along stream reaches will enhance vertical hydraulic gradient, whereas flushing flows can remove clogging layers and sustain sediment permeability. Our model is a first step to specifying mechanisms for recovery of lost vertical connectivity. Assessing results of river restoration using this approach at reach to catchment scales will provide scientific insights into the interplay of hydrology, fluvial geomorphology and river ecosystem function at appropriately broad scales.