Image interpolation, known also as inpainting or completion, represents the process of recovering the missing or highly deteriorated regions of the image, as plausibly as possible, by using the information achieved from the known surrounding areas. The inpainting techniques are divided into three main categories: structure-based, texture-based and combined reconstruction approaches. We consider only the structural image interpolation domain that comprises variational and partial di erential equation (PDE) - based inpainting models. A comprehensive overview of the state of the art nonlinear di usion-based inpainting techniques is provided here. Our own contributions to this image processing eld are also highlighted.