Advancements and challenges in rill formation, morphology, measurement and modeling

•Influence of soil properties on rill erosion is not adequately considered.•Study of timely changes in rill morphology and flow require advanced techniques.•Rill network requires more investigations to help prevent erosion at large scales.•Controlled experiments are case-specific and should be systematically integrated.•Rill erosion models are often simplified and require more knowledge on processes. Rill erosion is a small-scale but universally occurring phenomenon. Given its potential to concentrate into larger-scale erosion and its non-negligible contributions to soil loss, substantial research has been dedicated to understanding its processes. In this article, we conducted a holistic review of the major achievements in rill erosion research over the past few decades, mainly from the following perspectives: 1) Hydraulic parameters to describe rill development; 2) morphological indicators to represent rill morphology; 3) commonly used measuring methods for rill morphology and rill flow; and 4) advantages and limitations of rill erosion modelling. In each of the perspectives, we also identified the challenges faced by current rill erosion research. Concrete suggestions on the pressing needs to help advance rill erosion research in the future are further presented.