Energy and reliability of mobile nodes are the two important facets in a wireless sensor network and in real time monitoring applications. Sensor nodes with mobility have sparse energy resource thus achieving energy efficiency during routing has become a demanding need in mobile wireless sensor network. The recent advancements in Mobile Wireless Sensor Networks (MWSNs) has caught much attention as it offers great advantages in monitoring varied environmental niche by sensing physical processes. In this paper, the authors surveyed the available energy-efficient routing techniques like LEACH with mobility aware, hybrid multipath routing, latency and reliability-aware geographic routing and routing protocol based on dynamic slot reservation protocol.