Total solar irradiance and UV spectral solar irradiance has been monitored since 1978 through a succession of space missions. This is accompanied by the development of models aimed at replicating solar irradiance by relating the variability to solar magnetic activity. The Naval Research Laboratory Solar Spectral Irradiance (NRLSSI) and Spectral And Total Irradiance REconstruction for the Satellite era (SATIRE-S) models provide the most comprehensive reconstructions of total and spectral solar irradiance over the period of satellite observation currently available. There is persistent controversy between the various measurements and models in terms of the wavelength dependence of the variation over the solar cycle, with repercussions on our understanding of the influence of UV solar irradiance variability on the stratosphere. We review the measurement and modeling of UV solar irradiance variability over the period of satellite observation. The SATIRE-S reconstruction is consistent with spectral solar irradiance observations where they are reliable. It is also supported by an independent, empirical reconstruction of UV spectral solar irradiance based on Upper Atmosphere Research Satellite/Solar Ultraviolet Spectral Irradiance Monitor measurements from an earlier study. The weaker solar cycle variability produced by NRLSSI between 300 and 400 nm is not evident in any available record. We show that although the method employed to construct NRLSSI is principally sound, reconstructed solar cycle variability is detrimentally affected by the uncertainty in the SSI observations it draws upon in the derivation. Based on our findings, we recommend, when choosing between the two models, the use of SATIRE-S for climate studies.