We present a comprehensive description of the theory and practice of opacity calculations from the infrared to the ultraviolet needed to generate models of the atmospheres of brown dwarfs and extrasolar giant planets. Methods for using existing line lists and spectroscopic databases in disparate formats are presented, and plots of the resulting absorptive opacities versus wavelength for the most important molecules and atoms at representative temperature/ pressure points are provided. Electronic, rovibrational, bound-free, bound-bound, free-free, and collision-induced transitions and monochromatic opacities are derived, discussed, and analyzed. The species addressed include the alkali metals, iron, heavy metal oxides, metal hydrides, H 2 , H 2 O, CH 4 , CO, NH 3 , H 2 S, PH 3 , and representative grains. Once monochromatic absorption cross sections for all constituents have been derived, chemical abundances have to be obtained before the resulting product can be summed to obtain total opacities. Hence, we include a review of the thermochemistry, techniques, and databases needed to derive equilibrium abundances and provide some sample results.