Hot methane spectra are important in environments ranging from flames to the atmospheres of cool stars and exoplanets. A new spectroscopic line list, 10to10, for (12)CH4 containing almost 10 billion transitions is presented. This comprehensive line list covers a broad spectroscopic range and is applicable for temperatures up to 1,500 K. Previous methane data are incomplete, leading to underestimated opacities at short wavelengths and elevated temperatures. Use of 10to10 in models of the bright T4.5 brown dwarf 2MASS 0559-14 leads to significantly better agreement with observations and in studies of the hot Jupiter exoplanet HD 189733b leads to up to a 20-fold increase in methane abundance. It is demonstrated that proper inclusion of the huge increase in hot transitions which are important at elevated temperatures is crucial for accurate characterizations of atmospheres of brown dwarfs and exoplanets, especially when observed in the near-infrared.