Contemporarily, the researches of the quantum Hall effect (QAHE) leads an intensive potentiality of topological insulators and corresponding quantum computing. The QAHE was considered as the last member of the family of Hall effect. In this paper, the history and development of QAHE will be introduced, together with the theoretical prediction and experimental observations. The relative application of normal QAHE and high temperature QAHE are discussed for the potential guiding meaning. The

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... l of experimental observed QAHE may shed a light on guiding further explorations of QAHE and the state-of-art applicetions (e.g., quantum com).