A study of curvature along the contour provides important sources of information about the shape of an object. Knowledge of contour curvature allows for the perception of and interaction with 3D objects. In this review, we will explore the value of contour curvature in the field of neurophysiology, psychophysics, computer vision, and psychology. The serial consolidation of disjoint edges, oriented in a particular manner, into composited curves allows building of identifiable shapes in occluded natural environments [Hess1999, Wertheimer1923, Zucker1989, Feldman2001]. Examples are our ability to pick objects, sort and manage shapes otherwise hidden or confounded by occlusion in messy natural environments. Contour curvature has been intensively studied in psychology as it forms the first steps in 2D shape building which eventually becomes 3D object recognition in the human brain.