We consider an interface above an attractive hard wall in the complete wetting regime, and submitted to the action of an external increasing, convex potential, and study its delocalization as the intensity of this potential vanishes. Our main motivation is the analysis of critical prewetting, which corresponds to the choice of a linear external potential. We also present partial results on critical prewetting in the two dimensional Ising model, as well as a few (weak) results on pathwise estimates for the pure wetting problem for effective interface models.