Heterogeneous distributed computing environments are emerging for developing data-intensive (big data) applications that require to access huge data files. Therefore, effective data management like efficient access and data availability has become critical requirement in these systems. Data replication is an essential technique applied to achieve these goals through storing multiple replicas in a wisely manner. There are replication algorithms that address some metrics such as reliability, availability, bandwidth consumption, storage usage, response time. In this paper, we present different issues involved in data replication and discuss the key points of the recent algorithms with a tabular representation of all those features. The focus of the review is the existing algorithms of data replication that are based on the meta-heuristic techniques. This review will enable the readers to see that previous studies contributed response time to the data replication, but the contribution of the energy consumption and security improvement has not been considerable well. Moreover, the impact of meta-heuristic algorithms on data replication performance is investigated in a simulation study. Finally, open issues and future challenges have been presented in this research work.