Neural abstractive summarization models have led to promising results in summarizing relatively short documents. We propose the first model for abstractive summarization of single, longer-form documents (e.g., research papers). Our approach consists of a new hierarchical encoder that models the discourse structure of a document, and an attentive discourse-aware decoder to generate the summary. Empirical results on two large-scale datasets of scientific papers show that our model significantly outperforms state-of-the-art models.