The chemistry of oxidants and their precursors (oxidants*) plays a central role in outdoor environments but its importance in indoor air remains poorly understood. Ozone (O3) chemistry is important in some indoor environments and, until recently, ozone was thought to be the dominant oxidant indoors. There is now evidence that formation of the hydroxyl radical by photolysis of nitrous acid (HONO) and formaldehyde (HCHO) may be important indoors. In the past few years, high time-resolution measurements of oxidants* indoors have become more common and the importance of event-based release of oxidants* during activities such as cleaning has been proposed. Here we review the current understanding of oxidants* indoors, including drivers of the formation and loss of oxidants*, levels of oxidants* in indoor environments, and important directions for future research.