The variability of the solar UV irradiance has strong effects on the terrestrial atmosphere. In order to study the solar influence for times when no UV observations are available, it is necessary to reconstruct the variation of the UV irradiance with time on the basis of proxies. We present reconstructions of the solar UV irradiance based on the analysis of space-based and ground-based magnetograms of the solar disk going back to 1974. With COde for Solar Irradiance (COSI) we calculate solar intensity spectra for the quiet Sun and different active regions and combine them according to their fractional area on the solar disk, whereby their time-dependent contributions over the solar cycle lead to a variability in radiation. COSI calculates the continuum and line formation under conditions which are out of local thermodynamic equilibrium (non-LTE). The applied temperature and density structures include the chromosphere and transition region, which is particularly important for the UV. The reconstructions are compared with observations.