Traditional supervised machine learning algorithms are expected to have access to a large corpus of labeled examples, but the massive amount of data available in the modern world has made unlabeled data much easier to acquire than accompanying labels. Active learning is an extension of the classical paradigm intended to lessen the expense of the labeling process by allowing the learning algorithm to intelligently choose which examples should be labeled. In this dissertation, we demonstrate that the power to make adaptive label queries has benefits beyond reducing labeling effort over passive learning. We develop and explore several novel methods for active learning that exemplify these new capabilities. Some of these methods use active learning for a non-standard purpose, such as computational speedup, structure discovery, and domain adaptation. Others successfully apply active learning in situations where prior results have given evidence of its ineffectiveness. Specifically, we first give an active algorithm for learning disjunctions that is able to overcome a computational intractability present in the semi-supervised version of the same problem. This is the first known example of the computational advantages of active learning. Next, we investigate using active learning to determine structural properties (margins) of the data-generating distribution that can further improve learning rates. This is in contrast to most active learning algorithms which either assume or ignore structure rather than seeking to identify and exploit it. We then give an active nearest neighbors algorithm for domain adaptation, the task of learning a predictor for some target domain using mostly examples from a different source domain. This is the first formal analysis of the generalization and query behavior of an active domain adaptation algorithm. Finally, we show a situation where active learning can outperform passive learning on very noisy data, circumventing prior results that active learning cannot have a significant advantage over passive learning in high-noise regimes.