A wide variety of research applications require knowledge of total solar irradiance (TSI) and solar spectral irradiance (SSI) on time scales from minutes to centuries. The current satellite data record of TSI and ultraviolet SSI is 40 years long while observations of solar irradiance at visible wavelengths through the near-infrared span 15 years. In late 2017, the NASA Total and Spectral Solar Irradiance Sensor-1 (TSIS-1) mission was deployed on the International Space Station (ISS); these new TSI and SSI datasets are now extending the observational solar irradiance record with a planned 5-year mission. Recognizing the need for ongoing specification of solar irradiance, the National Centers for Environmental Information established the Solar Irradiance Climate Data Record (CDR) in 2014. The CDR includes a composite record of TSI observations and estimates of solar total and spectral irradiance variations during, and prior, to the space-based record based on the Naval Research Laboratory (NRL) models. Utilizing as inputs proxies of sunspot darkening and facular brightening, the models specify TSI and SSI annually since 1610 and daily since 1882. Both the observational composite and the model specifications are updated regularly and will eventually utilize the new TSIS-1 observations, both to extend the observational composite and to validate and improve the models. With the goal of establishing the utility of the NRL models in specifying the time and wavelength dependence of solar variability for the Solar Irradiance CDR, we compare the latest NRLTSI2 and NRLSSI2 modeled irradiances with observations, including composite records, and with independent models of solar irradiance variability. Our assessments quantify current understanding of solar irradiance variability on multiple timescales and identify areas where TSIS-1 observations are expected to provide improved understanding of solar irradiance variability. We use the following datasets in our comparisons: TSIS-1, Solar Radiation and Climate Experiment (SORCE), Ozone Monitoring Instrument (OMI), Solar Irradiance Data Exploitation (SOLID), Spectral and Total Irradiance Reconstructions for the Satellite Era (SATIRE-S), a three-dimensional extension of the SATIRE-S model (SATIRE-3D), and Empirical Irradiance Reconstruction (EMPIRE).