This paper presents a new deformable modeling strategy that is aimed at integrating shape and appearance in a unified space. If we think of traditional deformable models as "active contours" or "evolving curve fronts," the new deformable shape and appearance models that we propose are "deforming disks or volumes." Each model not only has boundary shape but also interior appearance. The model shape is implicitly embedded in a higher dimensional space of distance transforms and is thus represented by a distance map "image." This way, both the shape and the appearance of the model are defined in the pixel space. A common deformation scheme, that is, the free-form deformations (FFDs), parameterizes warping deformations of the volumetric space in which the model is embedded, hence simultaneously deforming both model boundary and interior. When applied to segmentation, a metamorphs model can be initialized by covering a seed region far from the object boundary, and then the model efficiently evolves and converges to an optimal solution. The model dynamics are derived in a unified variational framework that consists of edge-based and region-based energy terms, both of which are differentiable with respect to the common set of FFD parameters. As the model deforms, its interior appearance statistics are adaptively learned and, then, toward the next-step deformation, the model examines not only edge information but also its exterior region statistics to ensure that it only expands to new territory with consistent appearance statistics. The Metamorphs formulation also allows natural merging and competition of multiple models. We demonstrate the robustness of metamorphs by using both natural and medical images that have high noise levels, intensity inhomogeneity, and complex texture.