Gully erosion is a significant environmental concern globally. It reduces agricultural productivity, damages urban and rural infrastructure, degrades the quality of receiving waters, and can cause loss of life. In this review we synthesise contemporary models for the erosion of classical gullies An overview of erosion processes provides a context for modelling, and provides a clear delineation for models focussed on classical gullies versus smaller morphological systems. Mathematical models of classical gully erosion have been developed to predict gully initiation and growth, simulate the export of sediments from gullies, and inform land management practices. We identify and summarise 13 classical gully erosion models. These models are classified according to their purpose, mathematical approach, and the scale (spatial and temporal) at which they are applied. The models range from individual gully scale to continental, and from event to decadal timescales. We provide a flowchart to aid in gully erosion model selection based on the modelling objective and data availability. Finally, nine opportunities for the development of gully erosion models are identified: data acquisition, machine learning, sensitivity and uncertainty analysis, climate change risk analysis, model parameterisation and validation, land management implications, gully morphology, neglected processes, and inter-operability of models for catchment-scale applications.