In this paper, we present a study of a novel summarization problem, i.e., summarizing the impact of a scientific publication. Given a paper and its citation context, we study how to extract sentences that can represent the most influential content of the paper. We propose language modeling methods for solving this problem, and study how to incorporate features such as authority and proximity to accurately estimate the impact language model. Experiment results on a SIGIR publication collection show that the proposed methods are effective for generating impact-based summaries.