We report results of wetting on non-planar and heterogeneous surfaces calculated from an effective interfacial Hamiltonian model. The lack of translational invariance along the substrate induces a series of structural changes of the interface such as unbending and a number of non-thermodynamic singularities and can modify the location of the wetting transition. We show that the order of the wetting transition in the planar homogeneous system strongly affects the behaviour of the non-planar and heterogeneous surfaces.