Event argument extraction (EAE) aims to identify the arguments of an event and classify the roles that those arguments play. Despite great efforts made in prior work, there remain many challenges: (1) Data scarcity. (2) Capturing the long-range dependency, specifically, the connection between an event trigger and a distant event argument. (3) Integrating event trigger information into candidate argument representation. For (1), we explore using unlabeled data in different ways. For (2), we propose to use a syntax-attending Transformer that can utilize dependency parses to guide the attention mechanism. For (3), we propose a trigger-aware sequence encoder with several types of trigger-dependent sequence representations. We also support argument extraction either from text annotated with gold entities or from plain text. Experiments on the English ACE2005 benchmark show that our approach achieves a new state-of-the-art.