A great deal of research has been conducted on modeling and discovering communities in complex networks. In most real life networks, including social networks and bio-chemical networks, an object often participates in multiple overlapping communities. In view of this, recent research has focused on mining overlapping community structures in complex networks. The algorithms essentially materialize a snapshot of the overlapping communities in the network. This approach has three drawbacks, however. First, the mining algorithm uses the same global criterion to decide whether a subgraph qualifies as a community. In other words, the criterion is fixed and predetermined. But in reality, communities for different vertices may have very different characteristics. Second, it is costly, time consuming, and often unnecessary to find communities for an entire network. Third, the approach does not support dynamically evolving networks. In this paper, we focus on online search of overlapping communities, that is, given a query vertex, we find meaningful overlapping communities the vertex belongs to in an online manner. In doing so, each search can use community criterion tailored for the vertex in the search. To support this approach, we introduce a novel model for overlapping communities, and we provide theoretical guidelines for tuning the model. We present several algorithms for online overlapping community search and we conduct comprehensive experiments to demonstrate the effectiveness of the model and the algorithms. We also suggest many potential applications of our model and algorithms.