Abstract: We introduce the anomalous Hall effect and its intrinsic mechanism, and then discuss the quantized anomalous Hall effect (QAHE). From the viewpoint of topological order, we focus on the differences and relationships among the quantum Hall effect, quantum spin Hall effect, QAHE, and topological insulators. Finally, we discuss the proposal that QAHE can be realized in thin films made of magnetic topological insulators such as Bi2Se3, Bi2Te3 and Sb2Te3 doped with Cr or Fe.