We examine the capabilities of a unified, multi-task framework for three information extraction tasks: named entity recognition, relation extraction, and event extraction. Our framework (called DyGIE++) accomplishes all tasks by enumerating, refining, and scoring text spans designed to capture local (within-sentence) and global (cross-sentence) context. Our framework achieves state-of-the-art results across all tasks, on four datasets from a variety of domains. We perform experiments comparing different techniques to construct span representations. Contextualized embeddings like BERT perform well at capturing relationships among entities in the same or adjacent sentences, while dynamic span graph updates model long-range cross-sentence relationships. For instance, propagating span representations via predicted coreference links can enable the model to disambiguate challenging entity mentions. Our code is publicly available at https://github.com/dwadden/dygiepp and can be easily adapted for new tasks or datasets.