How to evaluate academic influence in a more objective and fair way has always been an important and concerned issue. The proposal of the H- index broke the original status quo of taking the impact factor as a single evaluation index, aroused extensive attention and discussion, and produced dozens of derivative indexes in the following years, which greatly promoted the field of scient metrics in-depth research and development. This paper introduces the H- index and its three representative derived indicators in detail. From the perspective of the citation distribution curve of scholars or units, the essence of these indicators is discussed, and the advantages and disadvantages of each are discussed. Finally, the research on the impact evaluation of academic output is prospected.