Induced Compton scattering can cause strong spectral distortion when the Thomson scattering optical depth τT exceeds 5 × 109 K/T, where T is the brightness temperature. Observations of intraday variability in several compact radio sources and direct brightness temperature measurements of ~ 1–4 × 1012 K from orbiting VLBI prompt a re-examination of this process. We seek observable signatures of induced scattering, using a model for non-linear radiative transfer on a lattice. Induced Compton scattering can significantly increase the brightness temperature at low frequencies and may lead to the formation of steep gradients in the spectrum, and angular discontinuities in the observed intensity. An ultracompact high-brightness core surrounded by a tenuous electron-scattering shell should thus show a faint halo whose spectrum peaks at a lower frequency than the core. Thicker shells can be strongly limb-brightened; frequency-dependent superluminal expansion is also possible. The strongest signatures of induced Compton scattering are strong spectral variation in the source structure and large, frequency-dependent, linear polarization. Under some conditions, stimulated Raman scattering off collective plasma waves, which has similar observational characteristics, may dominate over induced Compton scattering off individual electrons and screened ions. As yet, there is no compelling evidence that induced Compton scattering has been observed in compact radio sources. This implies a (model-dependent) upper limit on the Thomson optical depth of plasma in the vicinity of the source. Future VLBI observations, with greater dynamic range, may provide valuable tracers of dense ionized gas in active galactic nuclei. Infrared observations of blazars should be scrutinized for evidence of induced scattering.