Digital topology was developed by A. Rosenfeld in the late 1970s and early1980s for image processing. It can be traced back to Alexandroff and Hopf in 1935. In this talk, we will review some concepts and application algorithms of digital topology. We will first introduce digital connectivity and the Jordan curve theorem. Then, we will specifically discuss digital surfaces and digital manifolds. At the end, we will present the digital version of Gauss-Bonnet Theorem, the hole-counting formula of digital images, and data reconstruction using digital functions.