Connectivity describes the efficiency of material transfer between geomorphic system components such as hillslopes and rivers or longitudinal segments within a river network. Representations of geomorphic systems as networks should recognize that the compartments, links, and nodes exhibit connectivity at differing scales. The historical underpinnings of connectivity in geomorphology involve management of geomorphic systems and observations linking surface processes to landform dynamics. Current work in geomorphic connectivity emphasizes hydrological, sediment, or landscape connectivity. Signatures of connectivity can be detected using diverse indicators that vary from contemporary processes to stratigraphic records or a spatial metric such as sediment yield that encompasses geomorphic processes operating over diverse time and space scales. One approach to measuring connectivity is to determine the fundamental temporal and spatial scales for the phenomenon of interest and to make measurements at a sufficiently large multiple of the fundamental scales to capture reliably a representative sample. Another approach seeks to characterize how connectivity varies with scale, by applying the same metric over a wide range of scales or using statistical measures that characterize the frequency distributions of connectivity across scales. Identifying and measuring connectivity is useful in basic and applied geomorphic research and we explore the implications of connectivity for river management. Common themes and ideas that merit further research include; increased understanding of the importance of capturing landscape heterogeneity and connectivity patterns; the potential to use graph and network theory metrics in analyzing connectivity; the need to understand which metrics best represent the physical system and its connectivity pathways, and to apply these metrics to the validation of numerical models; and the need to recognize the importance of low levels of connectivity in some situations. We emphasize the value in evaluating boundaries between components of geomorphic systems as transition zones and examining the fluxes across them to understand landscape functioning.