The aim of active learning is to reduce the number of labeled examples needed to learn a good prediction rule by sequentially and adaptively selecting examples for labeling. The basic idea is to use knowledge gained from previously labeled examples to automatically select the most informative example(s) to label next. Active learning has received considerable attention in recent years, but there are relatively few results pertaining to nonparametric active learning. For instance, the problem of actively learning a linear classifier is well understood, but active learning for nonparametric decision boundaries is much less developed. This talk will review past work in nonparametric active learning theory and discuss a new approach that requires less stringent assumptions and is more practically applicable to learning nonparametric decision boundaries. The new approach also is suitable for active label prediction on graphs.