This systematic literature review explores the Fermatean Fuzzy Set (FFS) theory and its extensions, analyzing 135 relevant articles to address key research questions (RQs) in FFS literature. The study follows the SPAR-4-SLR protocol, providing a comprehensive overview of FFS publications, applications, methodologies, and research gaps. The review highlights the growing interest in FFS, its integration with other fuzzy sets like Intuitionistic Fuzzy Sets (IFS) and Pythagorean Fuzzy Sets (PFS), and its potential for handling uncertainty in decision-making. FFSs are characterized by cubic sums of membership and non-membership values, offering a more flexible and powerful framework for managing ambiguity compared to traditional fuzzy sets. The study identifies various applications of FFS in fields such as decision-making, risk evaluation, investment, emergency response, and renewable energy. It also examines the use of aggregation operators (AOs), linguistic sets, and extensions of FFS to enhance its applicability. The review discusses the advantages and limitations of different FFS methods, including TOPSIS, CRITIC, CODAS, COPRAS, and others, and highlights the importance of comparative analysis and sensitivity analysis in validating FFS-based approaches. The study also explores non-MCDM methods, such as distance measures and AOs, which are used to address complex decision-making problems. The findings reveal that FFSs are increasingly being applied in diverse domains, with a focus on improving decision-making processes through enhanced flexibility and accuracy. The review identifies key research gaps and future directions, emphasizing the need for further exploration of FFS extensions, integration with other methodologies, and the development of robust tools for practical applications. Overall, the study provides a comprehensive understanding of FFS theory, its applications, and its potential for advancing fuzzy logic in various fields.This systematic literature review explores the Fermatean Fuzzy Set (FFS) theory and its extensions, analyzing 135 relevant articles to address key research questions (RQs) in FFS literature. The study follows the SPAR-4-SLR protocol, providing a comprehensive overview of FFS publications, applications, methodologies, and research gaps. The review highlights the growing interest in FFS, its integration with other fuzzy sets like Intuitionistic Fuzzy Sets (IFS) and Pythagorean Fuzzy Sets (PFS), and its potential for handling uncertainty in decision-making. FFSs are characterized by cubic sums of membership and non-membership values, offering a more flexible and powerful framework for managing ambiguity compared to traditional fuzzy sets. The study identifies various applications of FFS in fields such as decision-making, risk evaluation, investment, emergency response, and renewable energy. It also examines the use of aggregation operators (AOs), linguistic sets, and extensions of FFS to enhance its applicability. The review discusses the advantages and limitations of different FFS methods, including TOPSIS, CRITIC, CODAS, COPRAS, and others, and highlights the importance of comparative analysis and sensitivity analysis in validating FFS-based approaches. The study also explores non-MCDM methods, such as distance measures and AOs, which are used to address complex decision-making problems. The findings reveal that FFSs are increasingly being applied in diverse domains, with a focus on improving decision-making processes through enhanced flexibility and accuracy. The review identifies key research gaps and future directions, emphasizing the need for further exploration of FFS extensions, integration with other methodologies, and the development of robust tools for practical applications. Overall, the study provides a comprehensive understanding of FFS theory, its applications, and its potential for advancing fuzzy logic in various fields.