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Author impact evaluation and prediction play a key role in determining rewards, funding, and promotion. In this paper, we first introduce the background of the author impact evaluation and prediction. Then, we review the recent developments of the author impact evaluation, including data collection, data pre-processing, data analysis, feature selection, algorithm design, and algorithm evaluation. Third, we provide an in-depth literature review on the author impact predictive models and the common evaluation metrics. Finally, we look into the representative research issues, including author impact inflation, unified evaluation standards, academic success gene, identification of the origins of hot streaks, and higher-order academic networks analysis. This paper should help the researchers obtain a broader understanding of the author impact evaluation and prediction and provides future research directions.