In the dynamic landscape of data streams, credit card Fraud Detection Systems (FDS) are increasingly challenged by fluctuations in the underlying data distribution and this phenomenon known as concept drift. This challenge especially exists in fraud analytics, where evolving consumer behaviour can significantly alter patterns over time. A key difficulty lies in distinguishing between true concept drift and evolution of fraud. The main challenge of concept drift is degradation of a predictive performance of a model. To overcome this challenge, financial institutions have developed a robust model by incorporating adaptability to the evolving nature of financial transactions. This has shown better results in prediction of frauds however, misclassification of a legitimate transaction as a fraud was often sacrificed. This study presents a systematic literature review on the incorporation of concept drift detection methods in FDS framework. The goal is to highlight the consequences of misclassification and further improvements to make a model robust under concept drift.