We compute models of the transmission spectra of planets HD 209458b, HD 189733b, and generic hot Jupiters. We examine the effects of temperature, surface gravity, and metallicity for the generic planets as a guide to understanding transmission spectra in general. We find that carbon dioxide absorption at 4.4 and 15 μm is prominent at high metallicity, and is a clear metallicity indicator. For HD 209458b and HD 189733b, we compute spectra for both one-dimensional and three-dimensional model atmospheres and examine the differences between them. The differences are usually small, but can be large if atmospheric temperatures are near important chemical abundance boundaries. The calculations for the 3D atmospheres, and their comparison with data, serve as constraints on these dynamical models that complement the secondary eclipse and light curve data sets. For planet HD 189733b in particular, substantial differences can exist between the transmission spectra of the leading and trailing hemispheres, which is an excellent probe of carbon chemistry. In thermochemical equilibrium, the cooler leading hemisphere is methane-dominated, and the hotter trailing hemisphere is CO-dominated, but these differences may be eliminated by non-equilibrium chemistry due to vertical mixing. For HD 189733b we attempt to constrain the temperature structure and molecular abundances in the atmosphere, based on matches to the available transmission spectra data sets, but show that some constraints are model dependent.