The Milky Way is a barred spiral galaxy, with physical properties inferred from various tracers informed by the extrapolation of structures seen in other galaxies. However, the distances of these tracers are measured indirectly and are model-dependent. We constructed a map of the Milky Way in three dimensions, based on the positions and distances of thousands of classical Cepheid variable stars. This map shows the structure of our Galaxy’s young stellar population and allows us to constrain the warped shape of the Milky Way’s disk. A simple model of star formation in the spiral arms reproduces the observed distribution of Cepheids.