The story of Titan's two most abundant volatile constituents, nitrogen and methane, is intertwined. The focus of this paper is the origin and evolution of Titan's nitrogen atmosphere and the cycle of methane from its production to destruction to replenishment. Relevant observational results from Cassini-Huygens, Voyager and the Earth as well as various hypotheses and models are reviewed. The origin of nitrogen by direct capture, and from dissociation of pri- mordial nitrogen-bearing molecules, especially ammonia, by impact, photolysis, thermal and other processes is evaluated. Similarly, the origin of methane from Saturn's sub-nebula or by water-rock reactions in Titan's interior is reviewed. The role of methane in regulating Titan's climate is noted, and similarities and differences between the methane cycle in Titan's troposphere and the hydrological cycle on Earth are discussed. The fate of methane in the stratosphere and the upper atmosphere/ionosphere is examined in order to evaluate the possibility and extent of an ocean of ethane, requirement of methane replenishment, and the role of product aerosols in maintaining Titan's nitrogen atmosphere.