This article surveys deformable models, a promising and vigorously researched computer-assisted medical image analysis technique. Among model-based techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics and approximation theory. They have proven to be effective in segmenting, matching and tracking anatomic structures by exploiting (bottom-up) constraints derived from the image data together with (top-down) a priori knowledge about the location, size and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the model-based image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, including segmentation, shape representation, matching and motion tracking.