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Understanding and modeling of solar-irradiance variability is important not only for solar physics but also for solar-terrestrial and solar-stellar studies. The latest irradiance measurements call into question aspects of currently-available empirical and semi-empirical models of solar-irradiance variability. A new generation of significantly more realistic physics-based irradiance models can now be created to incorporate recent advances in modeling and observing the solar atmosphere. This next generation of irradiance models will include new advances in MHD, surface flux transport, and radiative transfer simulations as well as new state-of-the-art solar data. By relying on physics-based understandings rather than merely empirical relationships established for the Sun, these new models will also allow more direct and physical extrapolations to other stars, opening a new regime for solar-stellar connection studies, as well as improved long-term estimates of historical solar variability.