Sediment connectivity has received increasing attention within the realm of soil erosion and sedimentation research. Characterization indices serve as pivotal tools for transitioning the assessment of connectivity from qualitative to quantitative. Compared to landscape connectivity and hydrological connectivity, research on sediment connectivity and the development of quantitative characterization indices are still in their early stages, highlighting the importance of systematically summarizing these advancements to uncover the challenges and opportunities. This paper comprehensively summarized and analyzed the advancements and trending themes in domestic and international research on sediment connectivity based on the perspective of a knowledge graph, and established a conceptual framework to thoroughly elucidate the components and influencing factors of sediment connectivity. Finally, the existing quantitative characterization indices for sediment connectivity were reviewed to summarize and discuss the current limitations and research barriers that urgently needed to be overcome. Commencing from the background of the research demand for sediment connectivity, the paper systematically organizes its conceptual framework, then discusses future development needs based on the current predicament, and emphasizes the necessity of further work in this field.