This paper argues that continual learning methods can benefit by splitting the capacity of the learner across multiple models. We use statistical learning theory and a thorough experimental analysis to show how multiple tasks can interact with each other in a highly non-trivial fashion when trained on a single model. The generalization error on a particular task can improve when it is trained with synergistic tasks, but can just as easily deteriorate when trained with competing tasks. This phenomenon motivates our method named Model Zoo which, inspired from the boosting literature, grows an ensemble of small models, each of which is trained during one episode of continual learning. We demonstrate dramatically large gains in accuracy on a wide variety of continual learning benchmarks.