Lasers and optical amplifiers based on solution-processable materials have been long-desired devices for their compatibility with virtually any substrate, scalability, and ease of integration with on-chip photonics and electronics. These devices have been pursued across a wide range of materials including polymers, small molecules, perovskites, and chemically prepared colloidal semiconductor nanocrystals, also commonly referred to as colloidal quantum dots. The latter materials are especially attractive for implementing optical-gain media as in addition to being compatible with inexpensive and easily scalable chemical techniques, they offer multiple advantages derived from a zero-dimensional character of their electronic states. These include a size-tunable emission wavelength, low optical gain thresholds, and weak sensitivity of lasing characteristics to variations in temperature. Here we review the status of colloidal nanocrystal lasing devices, most recent advances in this field, outstanding challenges, and the ongoing progress toward technological viable devices including colloidal quantum dot laser diodes.