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In this paper, we tackle a challenging problem inherent in a series of applications: tracking the influential nodes in dynamic networks. Specifically, we model a dynamic network as a stream of edge weight updates. This general model embraces many practical scenarios as special cases, such as edge and node insertions, deletions as well as evolving weighted graphs. Under the popularly adopted linear threshold model and independent cascade model, we consider two essential versions of the problem: finding the nodes whose influences passing a user specified threshold and finding the top-$k$ most influential nodes. Our key idea is to use the polling-based methods and maintain a sample of random RR sets so that we can approximate the influence of nodes with provable quality guarantees. We develop an efficient algorithm that incrementally updates the sample random RR sets against network changes. We also design methods to determine the proper sample sizes for the two versions of the problem so that we can provide strong quality guarantees and, at the same time, be efficient in both space and time. In addition to the thorough theoretical results, our experimental results on five real network data sets clearly demonstrate the effectiveness and efficiency of our algorithms. [ABSTRACT FROM PUBLISHER]