Carbon credit trading is a crucial strategy to achieve emission reduction goals at the lowest possible cost. However, carbon credit prices exhibit non-stationary and non-linear characteristics. This is compounded by the lack of a data-driven analysis of external factors that impact the future price of carbon. This article addresses this gap by conducting a comprehensive systematic literature review to identify the significant factors that contribute to the instability of the price of carbon credits. To achieve our goal, four electronic databases, namely IEEE Xplore, SpringerLink, ScienceDirect, and ACM, were searched systematically from January 1, 2005, to January 1, 2024. Upon conducting an exhaustive screening and analytical process, 41 articles were determined to meet the predefined quality assessment criteria, qualifying them for inclusion in this review. The study investigates the impact of 20 factors reported in the 41 shortlisted articles, including similar carbon markets, energy markets, environmental, macroeconomic, policy, social, economic, sustainable industry, and public awareness factors. Furthermore, the research methodically formulates and introduces a detailed taxonomy of the main factors affecting carbon credit prices, offering a structured approach to understanding the multifaceted influences on the carbon credit market. Researchers can build on these findings to further explore the dynamics of carbon markets and develop advanced models for price prediction and risk assessment.