  A comprehensive theory of interfacial fluctuation effects occurring at 2D
wedge (corner) filling transitions in pure (thermal disorder) and impure
(random bond-disorder) systems is presented. Scaling theory and the explicit
results of transfer matrix and replica trick studies of interfacial Hamiltonian
models reveal that, for almost all examples of intermolecular forces, the
critical behaviour at filling is fluctuation-dominated, characterised by
universal critical exponents and scaling functions that depend only on the
wandering exponent $\zeta$. Within this filling fluctuation (FFL) regime, the
critical behaviour of the mid-point interfacial height, probability
distribution function, local compressibility and wedge free energy are
identical to corresponding quantities predicted for the strong-fluctuation
(SFL) regime for critical wetting transitions at planar walls. In particular
the wedge free energy is related to the SFL regime point tension which is
calculated for systems with random-bond disorder using the replica trick. The
connection with the SFL regime for all these quantities can be expressed
precisely in terms of special wedge covariance relations which complement
standard scaling theory and restrict the allowed values of the critical
exponents for both FFL filling and SFL critical wetting.
