We approach instantaneous mapping, converting images to a top-down view of the world, as a translation problem. We show how a novel form of transformer network can be used to map from images and video directly to an overhead map or bird's-eye-view (BEV) of the world, in a single end-to-end network. We assume a 1-1 correspondence between a vertical scanline in the image, and rays passing through the camera location in an overhead map. This lets us formulate map generation from an image as a set of sequence-to-sequence translations. This constrained formulation, based upon a strong physical grounding of the problem, leads to a restricted transformer network that is convolutional in the horizontal direction only. The structure allows us to make efficient use of data when training, and obtains state-of-the-art results for instantaneous mapping of three large-scale datasets, including a 15\% and 30\% relative gain against existing best performing methods on the nuScenes and Argoverse datasets, respectively.