With the continual deployment of power-electronics-interfaced renewable energy resources, increasing privacy concerns due to deregulation of electricity markets, and the diversification of demand-side activities, traditional knowledge-based power system dynamic modeling methods are faced with unprecedented challenges. Data-driven modeling has been increasingly studied in recent years because of its lesser need for prior knowledge, higher capability of handling large-scale systems, and better adaptability to variations of system operating conditions. This paper discusses about the motivations and the generalized process of datadriven modeling, and provides a comprehensive overview of various state-of-the-art techniques and applications. It also comparatively presents the advantages and disadvantages of these methods and provides insight into outstanding challenges and possible research directions for the future.