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Quantifying success in science plays a key role in guiding funding allocations, recruitment decisions, and rewards. Recently, a significant amount of progresses have been made towards quantifying success in science. This lack of detailed analysis and summary continues a practical issue. The literature reports the factors influencing scholarly impact and evaluation methods and indices aimed at overcoming this crucial weakness. We focus on categorizing and reviewing the current development on evaluation indices of scholarly impact, including paper impact, scholar impact, and journal impact. Besides, we summarize the issues of existing evaluation methods and indices, investigate the open issues and challenges, and provide possible solutions, including the pattern of collaboration impact, unified evaluation standards, implicit success factor mining, dynamic academic network embedding, and scholarly impact inflation. This paper should help the researchers obtaining a broader understanding of quantifying success in science, and identifying some potential research directions.