New inorganic nonlinear-optical (NLO) materials are necessary for solid-state lasers to generate coherent radiation in the ultraviolet (UV) and deep-UV regions. The purpose of this Viewpoint is to describe the chemical and physical requirements for such materials, as well as the current state of the field. In addition, the "birefringence challenge" is described and a flowchart is presented for characterizing new second-harmonic-generation materials. Finally, several new materials are suggested that may have UV and/or deep-UV NLO applications.