A review of the theories of non-cortical strings and random surfaces

I review the basic properties of the theory of random surfaces. It is shown that the theory gives a correct description of strings in dimension d ≤ 1 and of matter fields with central charge c ≤ 1. In this region it coincides with the new results of Knizhnik, Polyakov and Zamolodchikov. Analytical and numerical results for the discretized model and for the standard continuum string model for d > 1 indicate a trivial theory in this region.