We present a survey of recent progress in the area of learning-based testing (LBT). The emphasis is primarily on fundamental concepts and theoretical principles, rather than applications and case studies. After surveying the basic principles and a concrete implementation of the approach, we describe recent directions in research such as: quantifying the hardness of learning problems, over-approximation methods for learning, and quantifying the power of model checker generated test cases. The common theme underlying these research directions is seen to be metrics for model convergence. Such metrics enable a precise, general and quantitative approach to both speed of learning and test coverage. Moreover, quantitative approaches to black-box test coverage serve to distinguish LBT from alternative approaches such as random and search-based testing. We conclude by outlining some prospects for future research.