Active learning is an important modern learning paradigm where the algorithm itself can ask for labels of carefully chosen examples from a large pool of unannotated data with the goal of minimizing human labeling effort. In this talk, I will present a computationally efficient, noise tolerant, and label efficient active learning algorithm for learning linear separators under log-concave and nearly log-concave distributions. Our technique exploits localization in several ways and can be thought of essentially solving an adaptively chosen sequence of convex optimization (specifically hinge loss minimization) problems around smaller and smaller bands around the current guess for the target. Surprisingly, our algorithms not only have label complexity that is much better than one can hope for in the classic passive learning scenario (where all the examples are annotated/labeled), but they have much better noise tolerance than previously known algorithms for this classic learning paradigm.