Protoplanetary discs set the initial conditions for planet formation. By combining observations with detailed modelling, it is possible to constrain the physics and chemistry in such discs. I have used the detailed thermo-chemical disc model ProDiMo to explore the characteristics of the gas in protoplanetary discs, particularly in Herbig Ae objects. I have assessed the ability of various observational data to trace the disc properties. This has involved a number of different approaches. Firstly I compute a series of disc models with increasing mass, in order to test the diagnostic powers of various emission lines, in particular as gas mass tracers. This approach is then expanded to a large multiparameter grid of ~ 10 5 disc models. I have helped to develop a tool for analysing and plotting the huge quantity of data presented by such a model grid. Following this approach I move on to a detailed study of the Herbig Ae star HD 163296, attempting to fit the large wealth of available observations simultaneously. These include new Herschel observations of the far-infrared emission lines, as well as interferometric CO observations and a large number of continuum data. This study addresses the topical issues of the disc gas/dust ratio, and the treatment of the disc outer edge. It explores the effects of dust settling, UV variability and stellar X-ray emission on the disc chemistry and line emission. There is possible evidence for gas-depletion in the disc of HD 163296, with the line emission enhanced by dust settling, which would indicate a later evolutionary stage for this disc than suggested by other studies. Finally, I work to improve the treatment of the gas heating/cooling balance in ProDiMo, by introducing a non-LTE treatment of the atomic hydrogen line transitions and bound-free continuum transitions. I explore the effects of this on the disc chemical and thermal structure, and assess its impact in terms of the observable quantities.