Image metamorphosis is simply a transformation that maps one image into another, altering both its shape and intensities; image deformation is a transformation that changes the shape of an image. These types of transformation have a wide range  of applications in remote sensing, medical imaging and, specially, in entertainm ent industry. This work attempts, through the use of adequate mathematical models, to conceptually describe and analyze digital image deformation and metamorphosis transformations. Moreover, the main techniques for obtaining these transformations are analyzed under this conceptual framework, and topics such as user interface, signal sampling and reconstruction, and two-pass transformations are discussed. Concluding, an implementation and some of its results and problems are presented.