Abstractive conversation summarization has received much attention recently. However, these generated summaries often suffer from insufficient, redundant, or incorrect content, largely due to the unstructured and complex characteristics of human-huma
n interactions. To this end, we propose to explicitly model the rich structures in conversations for more precise and accurate conversation summarization, by first incorporating discourse relations between utterances and action triples (who-doing-what'') in utterances through structured graphs to better encode conversations, and then designing a multi-granularity decoder to generate summaries by combining all levels of information. Experiments show that our proposed models outperform state-of-the-art methods and generalize well in other domains in terms of both automatic evaluations and human judgments. We have publicly released our code at https://github.com/GT-SALT/Structure-Aware-BART.