We investigate various 1D solid-on-solid (SOS) models using the transfer matrix method. The main results of the paper concern SOS interfaces near an attracting wall (line) when the end points of the interface are fixed away from the wall (line). We obtain typical interface shapes in the macroscopic scale. If attraction of the wall is strong enough, then a part of the interface is pinned to the wall (line) and the remaining parts of the interface form angles with the wall (line) the contact angles. Explicit expressions for the contact angles are derived. We show also that for a certain range of parameters the models exhibit reentrant wetting and drying. As a result the free energy of the SOS model as a function of temperature can have up to three points of nonanalyticity. The fluctuations of the SOS interface are investigated in detail. Quite unusual fluctuations are observed at the contact points -the points where unpinned and pinned parts of the interface meet.