  Direct measurements of the spectra of extrasolar giant planets are the keys
to determining their physical and chemical nature. The goal of theory is to
provide the tools and context with which such data are understood. It is only
by putting spectral observations through the sieve of theory that the promise
of exoplanet research can be realized. With the new {\em Spitzer} and HST data
of transiting "hot Jupiters," we have now dramatically entered the era of
remote sensing. We are probing their atmospheric compositions and temperature
profiles, are constraining their atmospheric dynamics, and are investigating
their phase light curves. Soon, many non-transiting exoplanets with wide
separations (analogs of Jupiter) will be imaged and their light curves and
spectra measured. In this paper, we present the basic physics, chemistry, and
spectroscopy necessary to model the current direct detections and to develop
the more sophisticated theories for both close-in and wide-separation
extrasolar giant planets that will be needed in the years to come as exoplanet
research accelerates into its future.
