This paper has been accepted for publication in IEEE Communications Surveys and Tutorials. The copyrights are with IEEE. Abstract: Content Delivery Networks (CDNs) have gained immense popularity over the years. Replica server placement is a key design issue in CDNs. It entails placing replica servers at meticulous locations, such that cost is minimized and Quality of Service (QoS) of end-users is satisfied. Many replica server placement models have been proposed in the literature of traditional CDN. As the CDN architecture is evolving through the adoption of emerging paradigms, such as, cloud computing and Network Functions Virtualization (NFV), new algorithms are being proposed. In this paper, we present a comprehensive survey of replica server placement algorithms in traditional and emerging paradigm based CDNs. We categorize the algorithms and provide a summary of their characteristics. Besides, we identify requirements for an efficient replica server placement algorithm and perform a comparison in the light of the requirements. Finally, we discuss potential avenues for further research in replica server placement in CDNs.