We study a problem of \emph{batch distribution drift} motivated by several applications, which consists of determining an accurate predictor for a target time segment, for which a moderate amount of labeled samples are at one's disposal, while leveraging past segments for which substantially more labeled samples are available. We give new algorithms for this problem guided by a new theoretical analysis and generalization bounds derived for this scenario. We further extend our results to the case where few or no labeled data is available for the period of interest. Finally, we report the results of extensive experiments demonstrating the benefits of our drifting algorithm, including comparisons with natural baselines. A by-product of our study is a principled solution to the problem of multiple-source adaptation with labeled source data and a moderate amount of target labeled data, which we briefly discuss and compare with.