For more than 90 years, solar extreme ultraviolet (EUV) irradiance modeling has progressed from empirical blackbody radiation formulations, through fudge factors, to typically measured irradiances and reference spectra as well as time-dependent empirical models representing continua and line emissions. A summary of recent EUV measurements by five rockets and three satellites during the 1980s is presented along with the major modeling efforts. The most significant reference spectra are reviewed and three independently derived empirical models are described. These include Hinteregger's 1981 SERF1, Nusinov's 1984 two-component, and Tobiska's 1990/1991 SERF2/EUV91 flux models. They each provide daily full-disk broad spectrum flux values from 2 to 105 nm at 1 AU. All the models depend to one degree or another on the long time series of the Atmosphere Explorer E (AE-E) EUV database. Each model uses ground- and/or space-based proxies to create emissions from solar atmospheric regions. Future challenges in EUV modeling are summarized including the basic requirements of models, the task of incorporating new observations and theory into the models, the task of comparing models with solar-terrestrial data sets, and long-term goals and modeling objectives. By the late 1990s, empirical models will potentially be improved through the use of proposed solar EUV irradiance measurements and images at selected wavelengths that will greatly enhance modeling and predictive capabilities. ¿ American Geophysical Union 1993