The H-index has been investigated in various studies; this index has many strengths that have made it popular. However, it also has weaknesses, due to which other indicators have been developed. This study aims to identify the strengths and weaknesses of the H-index and provide the minimum set of necessary components for developing a comprehensive author-level index. In this systematic literature review, Scopus, PubMed, Web of Science, Emerald, and ProQuest databases were searched to identify relevant studies. From the number of 14,253 retrieved studies, after two stages of screening, 81 studies were selected according to the eligibility criteria for data extraction. The findings of the study led to the identification of 15 strengths in the three categories of Quality Features, Simplicity, and Suitability, and 13 weaknesses in the six categories of Publications, Citations, Academic Age, Author Credit Allocation, Variety of Fields, and mathematical calculation for H-index. Finally, 28 components were identified as the minimum set of necessary components to develop a comprehensive author-level index to help evaluate researchers more realistically and fairly. The minimum components that need to be considered in developing a comprehensive author-level index can be proposed as follows: Quality Features, Simplicity, Suitability, Publications, Citations, Academic Age, Author Credit Allocation, Variety of Fields, and mathematical calculation.