To maintain the accuracy of supervised learning models in the presence of evolving data streams, we provide temporally-biased sampling schemes that weight recent data most heavily, with inclusion probabilities for a given data item decaying exponentially over time. We then periodically retrain the models on the current sample. This approach speeds up the training process relative to training on all of the data. Moreover, time-biasing lets the models adapt to recent changes in the data while-unlike in a sliding-window approach-still keeping some old data to ensure robustness in the face of temporary fluctuations and periodicities in the data values. In addition, the sampling-based approach allows existing analytic algorithms for static data to be applied to dynamic streaming data essentially without change. We provide and analyze both a simple sampling scheme (T-TBS) that probabilistically maintains a target sample size and a novel reservoir-based scheme (R-TBS) that is the first to provide both complete control over the decay rate and a guaranteed upper bound on the sample size, while maximizing both expected sample size and sample-size stability. The latter scheme rests on the notion of a “fractional sample” and, unlike T-TBS, allows for data arrival rates that are unknown and time varying. R-TBS and T-TBS are of independent interest, extending the known set of unequal-probability sampling schemes. We discuss distributed implementation strategies; experiments in Spark illuminate the performance and scalability of the algorithms, and show that our approach can increase machine learning robustness in the face of evolving data.