We report results of wetting on non-planar and heterogeneous surfaces calcu
lated from an effective interfacial Hamiltonian model. The lack of translat
ional invariance along the substrate induces a series of structural changes
of the interface such as unbending and a number of nonthermodynamic singul
arities and can modify the location of the wetting transition. We show that
the order of the wetting transition in the planar homogeneous system stron
gly affects the behaviour of the non-planar and heterogeneous surfaces.