New anchoring properties of liquid crystals on amorphous solid surfaces are presented. In nematics (N), angular anchoring is usually described in terms of the Rapini-Papoular form, assuming constant surface order parameter. We generalize this expression, predicting a decrease of surface order for strong surface disorientation. Recent experiments on anchorings of varying strength confirm these predictions. Conjectures for the angular anchoring of smectic A on a solid amorphous surface explain the two easy layer orientations, normal to the surface or parallel, faceting inside a small critical angle. Roughness-induced surface transitions are discussed. For antagonistic nematic and smectic anchorings, we expect, below the N–SAtransition, a bent nematic surface boundary layer, recently observed by smectization under an electric field. Finally, the positional anchoring strength of smectics is introduced in terms of shear induced surface melting, and confirmed by a recent observation of oscillating shear stresses at the layer period.