Human languages evolve to communicate about real-world events. Therefore, understanding events plays a critical role in natural language understanding (NLU). A key challenge to this mission lies in the fact that events are not just simple, standalone predicates. Rather, they are often described at different granularities, form different temporal orders, and directed by specific central goals in the context. This talk will present two parts of our recent studies on Event-Centric NLU. In the first part, I will talk about how logically-constrained learning can teach machines to understand temporal relations, membership relations and coreference of events (e.g., what should be the right process of “defend a dissertation”, “taking courses”, “publish papers” regarding “earning a PhD”?). The second part will talk about how to teach machines to understand the intents and central goals behind event processes (e.g, do machines understand that “ making a dough”, “adding toppings”, “preheating the oven” and “baking the dough” lead to “cooking pizza”?). I will also briefly discuss some recent advances and open problems in event-centric NLU, along with a system demonstration.