[1] New models of solar extreme ultraviolet (EUV) irradiance variability are constructed in 1 nm bins from 0 to 120 nm using multiple regression of the Mg II and F 10.7 solar activity indices with irradiance observations made during the descending phase of cycle 23. The models have been used to reconstruct EUV spectra daily since 1950, annually since 1610, to forecast daily EUV irradiance and to estimate future levels in cycle 24. A two-component model developed by scaling the observed rotational modulation of the two solar indices underestimates the solar cycle changes that the Solar EUV Experiment (SEE) reports at wavelengths shorter than 40 nm and longer than 80 nm. A three-component model implemented by including an additional term derived from the smoothed Mg II index better reproduces the measurements at all wavelengths. The three-component model is consistent with variations in the EUV energy from 0 to 45 nm that produces the far ultraviolet (FUV) terrestrial dayglow observed by the Global Ultraviolet Imager (GUVI). However, the spectral structure of this third component is complex, and its origin is uncertain. Analogous two-and three-component models are also developed with absolute scales determined by the NRLEUV2 spectrum of the quiet Sun rather than by the SEE average spectrum. Assessment of the EUV absolute spectrum and variability of the four different models indicate that during solar cycle 23, the EUV irradiance (0 to 120 nm) increased 100 ± 30%, from 2.9 ± 0.2 to 5.8 ± 0.9 mWm −2 , and may have been as low as 1.9 ± 0.5 mWm −2 during the 17th-century Maunder Minimum. Near the peak of upcoming solar cycle 24, EUV irradiance is expected to increase 40% to 80% above the 2008 minimum values.