The nature of Titan's surface has been a fascinating puzzle since the first definitive detection of an atmosphere in 1944. Pre-Voyager models of the surface based largely on cosmochemistry and the detection of atmospheric methane permitted a range of possibilities from clathrate hydrate to pure methane snow. The Voyager 1 flyby ruled out this last possibility but pointed to a mixed ocean of methane, higher hydrocarbons, and nitrogen about a kilometer in thickness. Subsequent ground-based radar observations reveal a reflective surface, inconsistent with pure light hydrocarbons. The variation in radar reflectivity from night to night is surprisingly high. Passive radiometry at centimeter wavelengths indicates a surface emissivity distinct from that of the icier Galilean satellites, suggesting that water ice does not dominate the surface either. Observations in the near-infrared region are consistent with dirty water ice as well as a suite of other materials, including areas of hydrocarbon seas. Reconciling the Voyager, radar and near-infrared data continue to be a challenge. Possibilities include the following: a hydrocarbon ocean, which is frothy or contains a significant amount of aerosol contaminants, maintained near the surface by stirring; an ocean stored in pore spaces of the ice regolith or in an aquiferlike system; an ocean that is somewhat smaller than estimated from the methane photolysis rate because of impact-driven chemistry. Models involving significant amounts of dry land exposed above a shallow ocean potentially run afoul of tidal constraints imposed by Titan's nonzero free orbital eccentricity. The Cassini/Huygens mission will investigate the nature of the surface through a variety of techniques and hopefully solve this long-standing planetary puzzle.