All stars exhibit intensity fluctuations over several timescales, from nanoseconds to years. These intensity fluctuations echo off bodies and structures in the star system. We posit that it is possible to take advantage of these echoes to detect, and possibly image, Earth-scale exoplanets. Unlike direct imaging techniques, temporal measurements do not require fringe tracking, maintaining an optically-perfect baseline, or utilizing ultra-contrast coronagraphs. Unlike transit or radial velocity techniques, stellar echo detection is not constrained to any specific orbital inclination. Current results suggest that existing and emerging technology can already enable stellar echo techniques at flare stars, such as Proxima Centauri, including detection, spectroscopic interrogation, and possibly even continent-level imaging of exoplanets in a variety of orbits. Detection of Earth-like planets around Sun-like stars appears to be extremely challenging, but cannot be fully quantified without additional data on micro- and millisecond-scale intensity fluctuations of the Sun. We consider survey missions in the mold of Kepler and place preliminary constraints on the feasibility of producing 3D tomographic maps of other structures in star systems, such as accretion disks. In this report we discuss the theory, limitations, models, and future opportunities for stellar echo imaging.