We consider a polymer brush composed of units of type P, at a solid substrate S in an incompatible binary A/L solvent mixture. At A/L coexistence the film thickness of the wetting component A depends mainly on the second virial coefficient v(AP) of polymer-polymer contacts in an A-rich phase: with increasing v(AP) the film thickness jumps from a microscopic to a mesoscopic value and then continues to grow proportionally to v(AP). The film grows smoothly without bounds when the fluid interface is further out than the segments of the brush chains can reach. This escape of the A-L interface from the brush coincides with the (second-order) wetting transition and occurs at v(AP)(W). Substrates covered by a polymer brush are excellent surfaces order to measure critical wetting because the wetting behavior can be tuned independently from the short-range interactions of the solvents with the solid substrate. For relatively thin brushes, van der Waals contributions can seriously modify these predictions. However, as the brush thickness is proportional to the chain length N, the relative contribution of these forces can be tuned; i.e., for a sufficiently large blush height the (long-range) van der Waals forces can be ignored. The wetting scenario has been elaborated by a numerical self-consistent-field theory for inhomogeneous polymer systems.