Concept drift means that the concept about which data is obtained may shift from time to time, each time after some minimum permanence. Except for this minimum permanence, the concept shifts may not have to satisfy any further requirements and may occur infinitely often. Within this work is studied to what extent it is still possible to predict or learn values for a data sequence produced by drifting concepts. Various ways to measure the quality of such predictions, including martingale betting strategies and density and frequency of correctness, are introduced and compared with one another. For each of these measures of prediction quality, for some interesting concrete classes, usefully established are (nearly) optimal bounds on permanence for attaining learnability. The concrete classes, from which the drifting concepts are selected, include regular languages accepted by finite automata of bounded size, polynomials of bounded degree, and exponentially growing sequences defined by recurrence relations of bounded size. Some important, restricted cases of drifts are also studied, e.g., the case where the intervals of permanence are computable. In the case where the concepts shift only among finitely many possibilities from certain infinite, arguably practical classes, the learning algorithms can be considerably improved.