Scattering by the interstellar medium of our Galaxy corrupts our view of distant compact radio sources and causes their emission to appear variable on intra-day time scales. I discuss precisely how interstellar scattering effects their radiation, and how we can harness scattering-induced variability to image these sources and learn about physics at the base of an AGN jet. I show how the application of this theory to several particular sources is raising some unsettling questions about the nature of intra-day variable sources themselves.