In Titan's atmosphere, the second most abundant constituent, methane, exists as a gas, liquid and solid, and cycles between the atmosphere and the surface. Similar to the Earth's hydrological cycle, Titan sports clouds, rain and lakes. Yet, Titan's cycle differs dramatically from its terrestrial counterpart, and reveals the workings of weather in an atmosphere that is 10 times thicker than the Earth's atmosphere, that is two orders of magnitude less illuminated, and that involves a different condensable. While ongoing measurements by the Cassini-Huygens mission are revealing the intricacies of the moon's weather, circulation, lake coverage and geology, knowledge is still limited by the paucity of observations. This review of Titan's methane cycle therefore focuses on measured characteristics of the lower atmosphere and surface that appear particularly perplexing or alien.