AbstractConnectivity has emerged as a significant conceptual framework for understanding the transfer of surface water and sediment through landscapes. The concept has been widely adopted in the field of catchment hydrology but has also been valuable to investigate rates of soil erosion by water and sediment export across landscapes. To study connectivity, we gathered a group of scientists that worked on synthesizing and consolidating all theories and aspects of connectivity research. Within the EU‐funded ESSEM COST Action CONNECTEUR (ES1306), five working groups were established: (a) theory, (b) measuring, (c) modelling, (d) indices, and (e) society. One of the outputs of this COST Action is this Special Issue where we have assimilated research on connectivity around the globe. The papers of the Special Issue demonstrate the continued interest in the role of connectivity as a conceptual framework for understanding the transfer of surface water and sediment through landscapes. This Special Issue shows that the connectivity concept widens the view of a researcher by having to look at more parts of a system than is done in most studies in the field of hydrology and sediment dynamics. It addresses the connections among different parts of a catchment system: the hillslope with the channel, the soil column with vegetation effects on runoff, and channel process with ecology.