A detailed literature survey of the diverse applications in which the SMARTS spectral radiation model has been involved during the last 25 years first provides an overview of the model's influential status over a broad range of scientific disciplines. An historical perspective gives details about the founding principles and evolution of the model. Its main modeling algorithms, regarding both absorption and scattering from various atmospheric constituents are described, highlighting the new developments in the model's latest version (2.9.8), and the possible verification of its atmospheric transmittance functions with observations from a Rotating Shadowband Spectroradiometer. The addition of new dust and smoke aerosol models now allows the quantification of the circumsolar irradiance within 10 degrees of sun center for a wide range of scattering conditions. The circumsolar ratio for a 2.5 degrees aperture angle is found approximate to 5 times larger with dust aerosols than with rural aerosols. The impact on the modeled spectral or broadband irradiance of selecting the newer default extraterrestrial (AM0) spectrum is found generally low, except in the UV where differences of approximate to 5% can be expected. The possibility of experimental realizations of the AM1.5D and AM1.5G standard reference spectra is investigated using spectroradiometers and other instruments at a high-elevation station in Colorado. The impacts on direct and global irradiance of using different input streams, different types of spectroradiometer, and two versions of SMARTS, are quantified. Usage of the SMARTS v2.9.8 is recommended for all demanding applications, possibly including future revisions of the standard reference spectra.