Comparing contours is an important problem in content-based image retrieval and object recognition. While humans can easily assess the similarity of two contours, a generic algorithm for approximating this ‘perceptual distance’ has proved elusive. We argue that a multiscale approach is required for this task and introduce a conceptually simple yet highly effective segment-based algorithm (Hierarchical Procrustes Matching (HPM)) which outperforms existing techniques on benchmark retrieval tests. Whereas HPM is designed to match complete contours, many real-world applications of shape matching involve partial occlusion and clutter. Probabilistic approaches to shape matching are particularly well-equipped to handle these problems, yet previous work in this area has focused on matching unordered point sets rather than contours. After reviewing the basic ideas behind probabilistic matching, we show how it can be extended to handle both contours and part-based shapes. In the final chapters of the thesis, we move from pair wise matching to the more complex problem of modelling shape classes. We present linear and nonlinear generative probabilistic models for both contours and unordered point sets and apply these to a variety of data sets. A particularly interesting finding is that the nonlinear contour model performs very well on a benchmark correspondence test relative to state-of-the-art alternatives.