Comparisons of TOPEX/POSEIDON tidal solutions derived from the data of the first year of this altimetric mission with the best previous models and with in situ data show very substantial improvements. Typically, the gain in accuracy for the major lunar tidal component M(2) is 30 percent in root-mean-square differences with reference to a standard ground truth data set from 78 stations distributed over the world ocean. This is a major step, obtained because of the high quality of these altimetric data. The combination of these data with recent numerical models through assimilation methods is pointing toward solutions at the ultimate limits of practical accuracy.