Despite excellent performance on stationary test sets, deep neural networks (DNNs) can fail to generalize to out-of-distribution (OoD) inputs, including natural, non-adversarial ones, which are common in real-world settings. In this paper, we present a framework for discovering DNN failures that harnesses 3D renderers and 3D models. That is, we estimate the parameters of a 3D renderer that cause a target DNN to misbehave in response to the rendered image. Using our framework and a self-assembled dataset of 3D objects, we investigate the vulnerability of DNNs to OoD poses of well-known objects in ImageNet. For objects that are readily recognized by DNNs in their canonical poses, DNNs incorrectly classify 97% of their pose space. In addition, DNNs are highly sensitive to slight pose perturbations. Importantly, adversarial poses transfer across models and datasets. We find that 99.9% and 99.4% of the poses misclassified by Inception-v3 also transfer to the AlexNet and ResNet-50 image classifiers trained on the same ImageNet dataset, respectively, and 75.5% transfer to the YOLOv3 object detector trained on MS COCO.