Image inpainting is an important research topic in the field of image processing. The objective of inpainting is to “guess” the lost information according to surrounding image information, which can be applied in old photo restoration, object removal and demosaicing. Based on the foundation of previous literature of image inpainting and image modeling, this paper provides an overview of the state-of-art image inpainting methods. This survey first covers mathematics models of inpainting and different kinds of image impairment. Then it goes to the main components of an image, the structure and the texture, and states how these inpainting models and algorithms deal with the two separately, using PDE’s method, exemplar-based method and etc. Afterwards sparse-representation-based inpainting and related techniques are introduced. Experimental analysis will be presented to evaluate the relative merits of different algorithms, with the measure of Peak Signal to Noise Ratio (PSNR) as well as direct visual perception.