The atmosphere of Titan is a complex system, where thermal structure, radiative transfer, dynamics, microphysics and photochemistry are strongly coupled together. The global climate model developed over the past 15 years at the Pierre-Simon Laplace Institute has been exploring these different couplings, and has demonstrated how they can help to interpret the observed atmospheric structure of Titan's lower atmosphere (mainly in the stratosphere and troposphere). This review discusses these interactions, and our current understanding of their role in the context of this model, but also of other available works. The recent Cassini results, and the importance of the production mechanisms for Titan's haze, have put forward the need to explore the mesosphere and the couplings between upper and lower atmosphere, as well as the current limits of available models.