Fraud is a serious crime that affects both financial institutions and individuals badly. The growth of the digital world and ease of access to the internet has led to the increase in fraudulent activities tremendously. With the evolution of technology, the methods of frauds has also evolved. In this paper we focuses on credit card fraud detection algorithms. Credit card frauds are increasing because of its wide usage and huge amount of credit limit. Credit cards are ubiquitous and integral part of online financial transactions. In this paper we mainly focuses on various credit card fraud detection algorithms stating their merits and demerits and also highlights the various issues and challenges in the various algorithms developed so far. Though Data Mining and Machine Learning techniques are used for credit card fraud detection but still there is a need of efficient technique for real time fraud detection. Ensemble learning, Deep Learning techniques works better in detecting real time fraud. Lack of availability of datasets, class imbalance in datasets, feature selection are major challenges in detecting credit card fraud. The study is useful to the researchers and scientists working in the area of credit card fraud detection algorithms.