This review article provides an overview of recent advances in the study and understanding of dynamics of excitons in semiconductor nanocrystals (NCs) or quantum dots (QDs). Emphasis is placed on the relationship between exciton dynamics and optical properties, both linear and nonlinear. We also focus on the unique aspects of exciton dynamics in semiconductor NCs as compared to those in bulk crystals. Various experimental techniques for probing exciton dynamics, particularly time-resolved laser methods, are reviewed. Relevant models and computational studies are also briefly presented. By comparing different materials systems, a unifying picture is proposed to account for the major dynamic features of excitons in semiconductor QDs. While the specific dynamic processes involved are material-dependent, key processes can be identified for all the materials that include electronic dephasing, intraband relaxation, trapping, and interband recombination of free and trapped charge carriers (electron and hole). Exciton dynamics play a critical role in the fundamental properties and functionalities of nanomaterials of interest for a variety of applications including optical detectors, solar energy conversion, lasers, and sensors. A better understanding of exciton dynamics in nanomaterials is thus important both fundamentally and technologically.