The performance evaluation of repairable systems is a critical area of study in reliability engineering. This review paper examines various mathematical models used to assess and predict the performance of repairable systems. The focus is on understanding the strengths, limitations, and applications of these models in real-world scenarios. Key models reviewed include the Homogeneous Poisson Process (HPP), Non-Homogeneous Poisson Process (NHPP), and Renewal Process, among others. Each model's theoretical foundations are discussed, along with practical examples to illustrate their application. The review also explores advancements in repairable systems modeling, such as Bayesian approaches and machine learning techniques, which offer enhanced predictive capabilities. Challenges in modeling, including data quality and parameter estimation, are highlighted to provide a comprehensive understanding of the current state of research. By synthesizing findings from various studies, this paper aims to guide researchers and practitioners in selecting appropriate models for specific contexts, ultimately contributing to improved maintenance strategies and system reliability. Future research directions are suggested, emphasizing the integration of emerging technologies and the need for robust validation methods to enhance model accuracy and applicability.