When one uses computers to process a continuous image, the image must be represented by a discrete image or digital image, i.e. it is approximated by discrete objects. The problem is how to introduce a satisfactory topology for this discrete structure, so that the discrete model can faithfully exhibit some relevant features (such as connectedness and boundary) of a continuous original. The aim of this talk is to give an introduction to topological approach to the problem. Then we discuss continuity of functions in discrete models and their applications.