We propose an unsupervised method to learn the 3D geometry of object categories by looking around them. Differently from traditional approaches, this method does not require CAD models or manual supervision. Instead, using only video sequences showing object instances from a moving viewpoint, the method learns a deep neural network that can predict several aspects of the 3D geometry of such objects from single images. The network has three components. The first is a Siamese viewpoint factorization network that robustly aligns the input videos and learns to predict the absolute viewpoint of the object from a single image. The second is a depth estimation network that performs monocular depth prediction. The third is a shape completion network that predicts the full 3D shape of the object from the output of the monocular depth prediction module. While the three modules solve very different task, we show that they all benefit significantly from allowing networks to perform probabilistic predictions. This results in a self-assessment mechanism which is crucial for obtaining high quality predictions. Our network achieves state-of-the-art results on viewpoint prediction, depth estimation, and 3D point cloud estimation on public benchmarks.