Abstract: The task of summarization often requires a non-trivial understanding of the given text at the semantic level. In this work, we essentially incorporate the constituent structure into the single document summarization via the Graph Neural Networks to learn the semantic meaning of tokens. More specifically, we propose a novel hierarchical heterogeneous graph attention network over constituency-based parse trees for syntax-aware summarization. This approach reflects psychological findings that humans will pinpoint specific selection patterns to construct summaries hierarchically. Extensive experiments demonstrate that our model is effective for both the abstractive and extractive summarization tasks on six benchmark datasets from various domains. Moreover, further performance improvement can be obtained by virtue of state-of-the-art pre-trained models. Lastly, we test our model for the code summarization task for border impact.