We present the results of a new series of nongray 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 H₂ at longer wavelengths and H₂O 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 (~1.05 μm), J (~1.2 μm), H (~1.6 μm), K (~2.2 μm), M (~5 μm), and N (~10 μm), 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 CH₄ and H₂ absorption. Furthermore, we conclude that for T_eff's below 1200 K most or all true metals may be sequestered below the photosphere, that an interior radiative zone is a generic feature of substellar objects, and that clouds of H₂O and NH₃ are formed for T_eff's below ~400 and ~200 K, respectively. This study is done for solar-metallicity objects in isolation and does not include the effects of stellar insulation. Nevertheless, it is a comprehensive attempt to bridge the gap between the planetary and stellar realms and to develop a nongray theory of objects from 0.3M_J ("Saturn") to 70M_J (~0.07 M). We find that the detection ranges for brown dwarf/EGP discovery of both ground- and space-based telescopes are larger than previously estimated.