Methods, systems, and apparatus, including computer programs encoded on computer storage media, for scalable continual learning using neural networks. One of the methods includes receiving new training data for a new machine learning task; training an active subnetwork on the new training data to determine trained values of the active network parameters from initial values of the active network parameters while holding current values of the knowledge parameters fixed; and training a knowledge subnetwork on the new training data to determine updated values of the knowledge parameters from the current values of the knowledge parameters by training the knowledge subnetwork to generate knowledge outputs for the new training inputs that match active outputs generated by the trained active subnetwork for the new training inputs.