  We show that continuous filling or wedge-wetting transitions are possible in
3D wedge-geometries made from (angled) substrates exhibiting first-order
wetting transitions and develop a comprehensive fluctuation theory yielding a
complete classification of the critical behaviour. Our fluctuation theory is
based on the derivation of a Ginzburg criterion for filling and also an exact
transfer-matrix analysis of a novel effective Hamiltonian which we propose as a
model for wedge fluctuation effects. The influence of interfacial fluctuations
is shown to be very strong and, in particular, leads to a remarkable universal
divergence of the interfacial roughness $\xi_{\perp}\sim (T_F-T)^{-1/4}$ on
approaching the filling temperature $T_F$, valid for all possible types of
intermolecular forces.
