We propose DeepV2D, an end-to-end deep learning architecture for predicting depth from video. DeepV2D combines the representation ability of neural networks with the geometric principles governing image formation. We compose a collection of classical geometric algorithms, which are converted into trainable modules and combined into an end-to-end differentiable architecture. DeepV2D interleaves two stages: motion estimation and depth estimation. During inference, motion and depth estimation are alternated and converge to accurate depth.