The term ultraviolet (UV) burst is introduced to describe small, intense, transient brightenings in ultraviolet images of solar active regions. We inventorize their properties and provide a definition based on image sequences in transition-region lines. Coronal signatures are rare, and most bursts are associated with small-scale, canceling opposite-polarity fields in the photosphere that occur in emerging flux regions, moving magnetic features in sunspot moats, and sunspot light bridges. We also compare UV bursts with similar transition-region phenomena found previously in solar ultraviolet spectrometry and with similar phenomena at optical wavelengths, in particular Ellerman bombs. Akin to the latter, UV bursts are probably small-scale magnetic reconnection events occurring in the low atmosphere, at photospheric and/or chromospheric heights. Their intense emission in lines with optically thin formation gives unique diagnostic opportunities for studying the physics of magnetic reconnection in the low solar atmosphere. This paper is a review report from an International Space Science Institute team that met in 2016-2017.