Routing techniques (RTs) play a critical role in modern computing systems that use network-on-chip (NoC) communication infrastructure within multiprocessor system-on-chip (MPSoC) platforms. RTs contribute greatly to the successful performance of NoC-based MPSoCs due to traffic congestion avoidance, quality-of-service assurance, fault handling and optimisation of power usage. This paper outlines our efforts to catalogue RTs, limitations, recommendations and key challenges associated with these RTs used in NoC-based MPSoC systems for the IoT domain. We utilized the PRISMA method to collect data from credible resources, including IEEE Xplore ®, ScienceDirect, Association for Computing Machinery and Web of Science. Out of the 906 research papers reviewed, only 51 were considered relevant to the investigation on NoC RTs. The study addresses issues related to NoC routing and suggests new approaches for in-package data negotiating. In addition, it gives an overview of the recent research on routing strategies and numerous algorithms that can be used for NoC-based MPSoCs. The literature analysis addresses current obstacles and delineates potential future avenues, recommendations, and challenges analyzing techniques to assess performance utilizing metrics within the TCCM framework.