The Minimum Description Length (MDL) approach to shape modelling is reviewed. It solves the point correspondence problem of selecting points on shapes defined as curves so that the points correspond across a data set. An efficient numerical implementation is presented and made available as open source Matlab code. The problems with the early MDL approaches are discussed. Finally the MDL approach is extended to an MDL Appearance Model, which is proposed as a means to perform unsupervised image segmentation.