Time-domain inversion of a three-dimensional inhomogeneous medium is formulated as a time-domain diffraction tomography. The scattered data are expanded into a spectrum of time-dependent plane waves using the slant-stack transform. It is then shown that each time-dependent plane-wave constituent in the data is directly related to the Radon transform of the medium's inhomogeneity along the direction that bisects the angle between the plane wave and the incident wave. This new tomograhic relation provides the basis for two inversion approaches: a Radon-space reconstruction and a time-dependent filtered backpropagation. Finally, the reconstruction errors due to the limited spacetime aperture are identified via analysis and a numerical example.