Strings, matrix models, and meanders

I briefly review the present status of bosonic strings and discretized random surfaces in D > 1 which seem to be in a polymer rather than stringy phase. As an explicit example of what happens, I consider the Kazakov-Migdal model with a logarithmic potential which is exactly solvable for any D (at large D for an arbitrary potential). I discuss also the meander problem and report some new results on its representation via matrix models and the relation to the Kazakov-Migdal model. A supersymmetric matrix model is especially useful for describing the principal meanders.