  We propose a non-local interfacial model for 3D short-range wetting at planar
and non-planar walls. The model is characterized by a binding potential
\emph{functional} depending only on the bulk Ornstein-Zernike correlation
function, which arises from different classes of tube-like fluctuations that
connect the interface and the substrate. The theory provides a physical
explanation for the origin of the effective position-dependent stiffness and
binding potential in approximate local theories, and also obeys the necessary
classical wedge covariance relationship between wetting and wedge filling.
Renormalization group and computer simulation studies reveal the strong
non-perturbative influence of non-locality at critical wetting, throwing light
on long-standing theoretical problems regarding the order of the phase
transition.
