Triple junctions (i.e., boundaries where three systems meet) constitute an interesting geometry for wetting phenomena. We study an Ising model of a triple junction, using Landau theory and scaling arguments. Various phenomena are predicted, from the familiar critical-point wetting to the opposite, critical-point dewetting. The latter prevails when fluctuations are taken into account. A comparison of wetting at triple junctions with wetting at walls and wetting at grain boundaries indicates an interesting universality. Critical-point wetting occurs whenever the surface displays (spontaneous or imposed) order at the bulk critical point.