Understanding how well critical source areas of water or sediment are connected to receiving surface waters, is an essential step towards improvement of land management. For this, it is important to quantify connectivity beyond the conceptual and proportional evaluation that most studies use connectivity for. Most studies measure only the potential of a landscape to allow connectivity to occur; or the connectivity that occurs at a given moment. This fact shows the two opportunities that will make it possible to monitor connectivity: assess the potential connectivity and the water and sediment fluxes through those landscapes. These components finally may result in the desired knowledge on the connectivity of the research area. In this chapter, we identify three spatial levels of connectivity: soil, hillslopes and catchments. In addition, to be able to measure and monitor connectivity the stocks and flow within every spatial level is introduced to allow for the identification of available techniques to actually assess connectivity at the given scale. The chapter ends with a set of key questions that need answering to make measuring connectivity on different scales reliable and useful.

The concept of connectivity appeared in several disciplines in the 1950s and 1960s, but did not enter geomorphology until the 1980s. The concept has led to profound insights into the behaviour of systems, and has had significant applications in management. Connectivity may be defined as a structured set of relationships between spatially and/or temporally distinct entities), or as the degree to which a system facilitates (or impedes) the movement of matter and energy through itself. The former definition focuses on the structure of the system, and the latter on the functioning of it. The two definitions give rise to the separate concepts of structural and functional connectivity. A fundamental difference between structural and functional connectivity lies in the fact that, whereas the former can be relatively easily measured, and a variety of tools exists to do so, the latter tends to be inferred from system behaviour, so that measurement is somewhat indirect. Notwithstanding the compelling arguments in favour of studying connectivity, the ability to apply the ideas of connectivity science in any discipline requires a number of challenges to be addressed.

In this chapter, the history and development of the concept of connectivity in geomorphology is presented. It further provides an overview of connectivity terminology, the underlying concepts and identifies the benefits of connectivity thinking for geomorphological research and applications. We further pursue the question of whether connectivity can be considered as key concept in geomorphology and address general key challenges in using connectivity to understand complex geomorphic systems.