As the Web hosts rich information about real-world entities, our information quests become increasingly entity centric. In this paper, we study the problem of focused harvesting of Web pages for entity aspects, to support downstream applications such as business analytics and building a vertical portal. Given that search engines are the de facto gateways to assess information on the Web, we recognize the essence of our problem as Learning to Query (L2Q)-to intelligently select queries so that we can harvest pages, via a search engine, focused on an entity aspect of interest. Thus, it is crucial to quantify the utilities of the candidate queries w.r.t. some entity aspect. In order to better estimate the utilities, we identify two opportunities and address their challenges. First, a target entity in a given domain has many peers. We leverage these peer entities to become domain aware. Second, a candidate query may overlap with the past queries that have already been fired. We account for these past queries to become context aware. Empirical results show that our approach significantly outperforms both algorithmic and manual baselines by 16% and 10% in F-scores, respectively.