We give an overview of work on several problems in optimization and data analysis arising from electrical power grids. In the first, we formulate a bilevel optimization problem to identify possible vulnerabilities by finding the attack that causes maximal disruption. In the second, we describe multivariate logistic regression (MLR) and deep learning approaches for identifying outages in a power grid from real-time sensor network data. We show that when these classifiers are trained to recognize the "signature" of outages under a variety of network conditions, they can identify outages correctly in the vast majority of cases. An extension of our approach can be used to determine optimal location of a limited number of sensors.