We review recent advances concerning the nature of fluctuation effects occurring at continuous filling transitions pertinent to fluid adsorption in wedge geometries. Unlike continuous (critical) wetting transitions for planar interfaces which are an extremely rare experimental phenomena, continuous filling transitions should be easily observable in the laboratory since they can occur even if the underlying wetting transition is first-order. We argue that interfacial fluctuation effects at filling transitions are extremely strong and lead to a remarkable universal divergence of the interfacial roughness xi perpendicular to similar to (T-F - T) (-1/4) on approaching the transition temperature TF, valid for all types of intermolecular forces. The results of renormalisation group and transfer matrix calculations of a novel interfacial model yielding a complete classification of the critical exponents for all dimensions and ranges of forces are given.