The increasing availability of data and advances in computation have spurred the development of data-driven approaches for modeling complex dynamical systems. These approaches are based on the idea that the underlying structure of a complex system can be discovered from data using mathematical and computational techniques. They also show promise for addressing the challenges of modeling high-dimensional, nonlinear systems with limited data. In this research expository, the state of the art in data-driven approaches for modeling complex dynamical systems is surveyed in a systemic way. First the general formulation of data-driven modeling of dynamical systems is discussed. Then several representative methods in feature engineering and system identification/prediction are reviewed, including recent advances and key challenges.