Credit card fraud is a significant concern for financial institutions and cardholders alike. As fraudulent activities become more sophisticated, traditional rule-based approaches struggle to keep up. This has led to the adoption of machine learning techniques for fraud detection, which have shown promising results. However, the dynamic nature of credit card fraud poses a challenge due to the concept drift phenomenon. Concept drift refers to the changes in the underlying data distribution over time, requiring models to adapt and evolve to maintain their effectiveness. This research paper aims to provide a comprehensive comparative review of credit card fraud detection methods using machine learning and concept drift techniques. This literature review provides an overview of relevant studies comparing credit card fraud detection using machine learning techniques and concept drift handling methods. The paper evaluates the performance, strengths, and limitations of various approaches in addressing credit card fraud detection under concept drift scenarios.