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We present the results of a new series of non-gray calculations of the atmospheres, spectra, colors, and evolution of extrasolar giant planets (EGPs) and brown dwarfs for effective temperatures below 1300 K. This theory encompasses most of the mass/age parameter space occupied by substellar objects and is the first spectral study down to 100 K. These calculations are in aid of the multitude of searches being conducted or planned around the world for giant planets and brown dwarfs and reveal the exotic nature of the class. Generically, absorption by H_2 at longer wavelengths and H_2O opacity windows at shorter wavelengths conspire to redistribute flux blueward. Below 1200 K, methane is the dominant carbon bearing molecule and is a universal diagnostic feature of EGP and brown dwarf spectra. We find that the primary bands in which to search are $Z$ (\sim 1.05 \mic), $J$ (\sim 1.2 \mic), $H$ (\sim 1.6 \mic), $K$ (\sim 2.2 \mic), $M$ (\sim 5 \mic), and $N$ (\sim 10 \mic), that enhancements of the emergent flux over blackbody values, in particular in the near infrared, can be by many orders of magnitude, and that the infrared colors of EGPs and brown dwarfs are much bluer than previously believed. In particular, relative to $J$ and $H$, the $K$ band flux is reduced by CH_4 and H_2 absorption. Furthermore, we derive that for T_{eff}s below 1200 K most or all true metals are sequestered below the photosphere, that an interior radiative zone is a generic feature of substellar objects, and that clouds of H_2O and NH_3 are formed for T_{eff}s below \sim 400 K and \sim 200 K, respectively. This study is done for solar-metallicity objects in isolation and does not include the effects of stellar insolation. Nevertheless, it is an attempt to bridge the gap between the planetary and stellar realms and to develop a non-gray theory of objects from 0.3 \mj (``saturn'') to 70 \mj ($\sim$0.07 \mo). We find that the detection ranges for brown dwarf/EGP discovery of both ground-- and space-based telescopes are larger than previously estimated.