Meandering channels are ubiquitous on the surface of the Earth, both on land and on the seafloor. Although there is a large volume of published research on meandering, relatively simple questions – like the prediction of migration rates – are still considered highly complex problems with no simple solutions. A comparison of a simple curvature-based model of meandering with measurements from rivers and submarine channels suggests that, in systems unaffected by significant variation in erodibility, migration rates can be predicted relatively well, based on channel curvature alone. Plan-view meandering patterns in nature, both fluvial and submarine, show many of the characteristics of this model: a spatial phase lag between curvature and migration that has a characteristic length and results in autogenic downstream translation of many meander bends and in deposition of counter point bars. If along-channel changes in slope are added to the model, the implications of the 3D geometry for incising and aggrading channels become obvious as well. We use open-source code to visualize the 3D geometry and temporal evolution of the deposits of both subaerial and submarine meandering flows.