Deformable models are a popular and vigorously researched model-based approach to computerassisted medical image analysis. The widely recognized efficacy of deformable models stem from their ability to segment, match and track imagesof 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 structures of interest. Deformable models are capable of accomodating the often significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that allow medical scientists and practitioners to bring their expertise to bear on the model-based image interpretation task as necessary. In this paper we will review deformable models and present some recent developments in the methodology, including topologically adaptable deformable models, an approach that permits segmentation and reconstruction of topologically complex anatomical structures.