The advent of big data offers unprecedented opportunities for data-driven discovery and decision-making in virtually every area of human endeavor. In this talk, we zoom in to the applications of smart grid, which refers to the next generation electrical power grid that aims to provide reliable, efficient, secure, and quality energy generation/distribution/consumption using modern information, communications, and electronics technology. We further zoom in to study two specific cases. First, supported by local utility companies through electric power analytics consortium, we analyze real smart meter big data for load profiling and smart pricing. We employ techniques such as Bayesian nonparametric learning, sublinear algorithm, and deep learning. Second, we investigate how to solve Security-constrained Optimal Power Flow (SCOPF) Problem, through sparse optimization and alternating direction method of multipliers (ADMM). Finally, other research activities of our group will also be briefly described.