Infrared and millimeter-wave continuum surveys have placed strong constraints on the evolutionary timescales of circumstellar disks and any attendant planetary system. Rather less is known about the nature of the gas in protoplanetary accretion disks and how it may evolve with time. This talk will summarize recent millimeter-wave aperture synthesis studies of a suite of molecules in a small sample of the disks encircling T Tauri and Herbig Ae stars, and highlight future possibilities in both the near- and far-term. Probing the inner, planet-forming region of such disks is not presently possible at (sub)millimeter wavelengths, but high resolution spectroscopy in the mid-infrared with 8-10m class telescopes and with the Spitzer Space telescope InfraRed Spectrograph (IRS) is beginning to address this pivotal environment. The available data have been analyzed with detailed two-dimensional Monte Carlo radiative transfer codes, and the results of these analyses will be compared with the predictions of theoretical chemical models of protoplanetary disks.