Routing algorithms play a vital role in network communication for information technology. Classic networks usually exploit distributed routing algorithms which pave the way to issues in controlling the network paths and accessing the data in concern with the global topology. The recently developed Software Defined Networking (SDN) is flexibly scalable and is more cost-efficient for operators and vendors of information technology. Software-defined networking is a new type of network with emerging ideas and the ability to adapt network parameters. To adapt to the changing environment the data processing (data plane) and the logic processing (control plane) layers are separated in SDN. The separation in the data plane and control plane improved the traffic and routing performance of the network. The applications of SDN are accelerating in the optical network, vehicular network, Internet-of-Things, underwater communication, Adhoc network, and wireless sensor network applications. The routing mechanism of data packets varies in accordance with the application to meet the quality of service and the quality of experience of the users. This article provides an in-depth analysis of the various routing algorithms used in different communication links like unicast and multicast communication and also discusses the merits and demerits availed of it based on the most imperative and essential parameters. A variety of research articles in the field have been chosen which were published during the period from 2015 to 2022. This research investigation would spur the research community of network communication towards more novel methodologies of SDN routing algorithms.