Direct measurements of the radii and masses of exoplanets, and indirect measurements of their temperatures, temperature profiles, and compositions have inaugurated the era of the remote sensing and characterization of planets beyond the solar system. Understanding a planet's atmosphere is a necessary condition for understanding not only the planet itself, but also its formation, structure, evolution, and habitability, This puts a premium on obtaining spectra, and developing credible interpretative tools with which to retrieve vital planetary information. However, for exoplanets these twin goals are far from being realized. In this talk, I review the current status of exoplanet theory and remote sensing via photometry and low-resolution spectroscopy. I highlight the limitations in our knowledge of compositions, thermal profiles, and the effects of stellar irradiation, focussing on, but not restricted to, transiting giant planets. I suggest that the true function of the recent past of exoplanet atmospheric research has been not to constrain planet properties for all time, but to train a new generation of scientists that, by rapid trial and error, is fast establishing a solid future foundation for a robust science of exoplanets.