With the continuous advances in mobile wireless sensor networks (MWSNs), the research community has responded to the challenges and constraints in the design of these networks by proposing efficient routing protocols that focus on particular performance metrics such as residual energy utilization, mobility, topology, scalability, localization, data collection routing, Quality of Service (QoS), etc. In addition, the introduction of mobility in WSN has brought new challenges for the routing, stability, security, and reliability of WSNs. Therefore, in this article, we present a comprehensive and meticulous investigation in the routing protocols and security challenges in the theory of MWSNs which was developed in recent years.