The art of image restoration and completion has entered a new phase thanks to digital technology. Indeed, virtual restoration is sometimes the only feasible option available to us, and it has, under the name 'inpainting', grown, from methods developed in the mathematics and computer vision communities, to the creation of tools used routinely by conservators and historians working in the worlds of fine art and cinema. The aim of this book is to provide, for a broad audience, a thorough description of imaging inpainting techniques. The book has a two-layer structure. In one layer, there is a general and more conceptual description of inpainting; in the other, there are boxed descriptions of the essentials of the mathematical and computational details. The idea is that readers can easily skip those boxes without disrupting the narrative. Examples of how the tools can be used are drawn from the Fitzwilliam Museum, Cambridge collections.