Wetting transitions, in which a fluid wets the interface between two fluid phases, are defined. There may be first, second, and higher order transitions. The line tension, an excess free energy per unit length of a three-phase contact line, and the boundary tension, another excess free energy associated with the boundary of two surface phases at the prewetting transition, are also defined. Mean-field density functional models of the fluid interfaces are introduced and their results on the wetting transitions, the line and boundary tensions, and the fluid structures in the three-phase contact region are presented.