Batch training of machine learning models based on neural networks is well established, whereas, to date, streaming methods are largely based on linear models. To go beyond linear in the online setting, nonparametric methods are of interest due to their universality and ability to stably incorporate new information via convexity or Bayes's rule. Unfortunately, when applied online, nonparametric methods suffer a "curse of dimensionality," which precludes their use: their complexity scales at least with the time index. We survey online compression tools that bring their memory under control and attain approximate convergence. The asymptotic bias depends on a compression parameter that trades off memory and accuracy. Applications to robotics, communications, economics, and power are discussed as well as extensions to multiagent systems.