This paper studies the problem of dynamic relationship and event discovery. A large body of previous work on relation extraction focuses on discovering predefined and static relationships between entities. In contrast, we aim to identify temporally defined (e.g., co-bursting) relationships that are not predefined by an existing schema, and we identify the underlying time constrained events that lead to these relationships. The key challenges in identifying such events include discovering and verifying dynamic connections among entities, and consolidating binary dynamic connections into events consisting of a set of entities that are connected at a given time period. We formalize this problem and introduce an efficient end-to-end pipeline as a solution. In particular, we introduce two formal notions, global temporal constraint cluster and local temporal constraint cluster, for detecting dynamic events. We further design efficient algorithms for discovering such events from a large graph of dynamic relationships. Finally, detailed experiments on real data show the effectiveness of our proposed solution.