The concept of connectivity has been the subject of a great deal of recent research and provided new insights and breakthroughs on runoff generation processes and watershed biogeochemistry. However, a consensus definition and cohesive mathematical framework that would permit the consistent quantification of hydrologic connectivity, the examination of the interrelationships between water and material (e.g., sediment and chemicals) connectivity, or rigorous study intercomparison, have not been presented by the water resource community. Building on previous conceptualizations and site‐specific or process‐specific metrics, this paper aimed to review the current state of science on hydrologic connectivity and its role in water‐mediated connectivity of material such as solutes and sediment before introducing a conceptual and a mathematical connectivity assessment framework. These frameworks rely on the quantification of Time scales, Thresholds, Excesses and Losses related to water and water‐mediated material transport dynamics and are referred to as the T‐TEL method. Through a small case study, we show how the T‐TEL method allows a wide range of properties to be quantified, namely the occurrence, frequency, duration, magnitude, and spatial extent of water and water‐mediated material connectivity. We also propose a research agenda to refine the T‐TEL method and ensure its usefulness for facilitating the research and management of connectivity in pristine and human‐impacted landscapes.