Many learning algorithms generate complex models that are difficult for a human to interpret, debug, and extend. In this paper, we address this challenge by proposing a new learning paradigm called correctable learning, where the learning algorithm receives external feedback about which data examples are incorrectly learned. We define a set of metrics which measure the correctability of a learning algorithm. We then propose a simple and efficient correctable learning algorithm which learns local models for different regions of the data space. Given an incorrect example, our method samples data in the neighborhood of that example and learns a new, more correct local model over that region. Experiments over multiple classification and ranking datasets show that our correctable learning algorithm offers significant improvements over the state-of-the-art techniques.