The Image Puzzle problem explores the reconstruction of images from a collection of rectangular pieces - or tiles - that do not overlap. The assembly of these puzzles is a challenging task even for human beings and is known to be an NP-complete problem. Several assembly challenges can be considered: unknown tile orientation, unknown original image size, missing or misaligned tiles, and degraded edges. The objective of the talk is to explore the automatic assembly methods present in the literature, considering each challenge, as well as its applications.