Influence analysis aims at detecting influential vertices in networks and utilizing them in cost-effective business strategies. Influence analysis in large-scale networks is a key technique in many important applications ranging from viral marketing and online advertisement to recommender systems, and thus has attracted great interest from both academia and industry. Early investigations on influence analysis often assume static networks. However, it is well recognized that real networks like social networks and the web network are not static but evolve rapidly over time. Thus, to make the results of influence analysis in real networks up-to-date, we have to take network evolution into consideration. Incorporating evolution of networks into influence analysis raises many new challenges, since an evolving network often updates at a fast rate and, except for the network owner, the evolution is usually even not entirely known to people. In this survey, we provide an overview on recent research in influence analysis in evolving networks, which has not been systematically reviewed in literature. We first revisit mathematical models of evolving networks and commonly used influence models. Then, we review recent research in five major tasks of evolving network influence analysis. We also discuss some future directions to explore.