Cold atomic gas, observable in the neutral hydrogen (HI) 21cm line, plays a crucial role in the evolution of interstellar matter in galaxies. The gas in galactic disks (including our own Galaxy) occurs in a wide range of temperatures and densities, most of which are unsuitable for star formation. Somehow, the warmer, diffuse atomic clouds are collected into colder, denser molecular clouds that can collapse under their own gravity. Compared to other phase transitions like photodissociation or recombination, molecular condensation is not easy to observe. However, 21cm-line HI self-absorption (HISA) appears to trace precisely this stage of cloud evolution by revealing the coldest atomic gas as 3-dimensional shadows against warmer background HI emission. The HISA phenomenon has been known for decades, but has been brought into sharp focus in recent years by new surveys with large single-dish telescopes like the Arecibo 305-meter and interferometers like the Very Large Array. I will review the findings of these surveys and the promise of new efforts with future instrumentation.