We introduce an algorithm, SVM-IS, for structured SVM learning that is computationally scalable to very large datasets and complex structural representations. We show that structured learning is at least as fast-and often much faster-than methods based on binary classification for problems such as deformable part models, object detection, and multiclass classification, while achieving accuracies that are at least as good. Our method allows problem-specific structural knowledge to be exploited for faster optimization by integrating with a user-defined importance sampling function. We demonstrate fast train times on two challenging large scale datasets for two very different problems: Image Net for multiclass classification and CUB-200-2011 for deformable part model training. Our method is shown to be 10-50 times faster than SVMstruct for cost-sensitive multiclass classification while being about as fast as the fastest 1-vs-all methods for multiclass classification. For deformable part model training, it is shown to be 50-1000 times faster than methods based on SVMstruct, mining hard negatives, and Pegasos-style stochastic gradient descent. Source code of our method is publicly available.