Protoplanetary disks are found to orbit around low- and intermediate-mass stars. Current theories predict that these disks are the likely sites for planet formation. In this review, we summarize the improvement in our knowledge of their observed molecular properties since Protostars and Planets IV (PPIV). This is timely since a new facility, the Submillimeter Array (SMA), has recently begun operation and has opened the submillimeter atmospheric windows to interferometry, allowing studies of warmer gas and dust in disks at subarcsecond resolution. Using results from the IRAM array and the SMA, we focus on two complementary main topics: (1) the determination of the physical structure of the disks from multitransition CO isotopic analysis of high-angular-resolution millimeter interferometric data and (2) the observations of molecules other than CO (and isotopes), which enable investigations of the chemistry in protoplanetary disks. In particular, we emphasize how to handle the available data to provide relevant constraints on the thermal, physical, and chemical structure of the disks as a function of radius, within the current limitations in sensitivity and angular resolution of the existing arrays. These results suggest the importance of photodissociation effects and X-ray heating. They also reveal unexpected results, such as the discovery of non-Keplerian rotation in the AB Aur disk. We also discuss how to extrapolate these results in the context of the tremendous capabilities of the ALMA project currently under construction in Chile.Read less <