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In the post-Cloud era, the proliferation of Internet of Things (IoT) has pushed the horizon of Edge computing, which is a new computing paradigm with data processed at the edge of the network. As the important systems of Edge computing, wireless sensor and actuator networks (WSANs) play an important role in collecting and processing the sensing data from the surrounding environment as well as taking actions on the events happening in the environment. In WSANs, in-network data storage and information discovery schemes with high energy efficiency, high load balance and low latency are needed because of the limited resources of the sensor nodes and the real-time requirement of some specific applications, such as putting out a big fire in a forest. In this article, the existing schemes of WSANs on data storage and information discovery are surveyed with detailed analysis on their advancements and shortcomings, and possible solutions are proposed on how to achieve high efficiency, good load balance, and perfect real-time performances at the same time, hoping that it can provide a good reference for the future research of the WSANs-based Edge computing systems.