The wetting of soft polymer substrates brings in multiple complexities as compared to the wetting on rigid substrates. The contact angle of the liquid is no longer governed by Young's law, but is affected by the substrate's bulk and surface deformations. On top of that, elastic interfaces exhibit a surface energy that depends on how much they are stretched -- a feature known as the Shuttleworth effect (or as surface-elasticity). Here we present two models by which we explore the wetting of drops in the presence of a strong Shuttleworth effect. The first model is macroscopic in character and consistently accounts for large deformations via a neo-Hookean elasticity. The second model is based on a mesoscopic description of wetting, using a reduced description of the substrate's elasticity. While the second model is more empirical in terms of the elasticity, it enables a gradient dynamics formulation for soft wetting dynamics.