Internal Structure of Black Holes

We present a number of qualitative arguments which strongly suggest that extremal dyonic black holes in the 4--dimensional low energy, classical field theory limit of toroidally compactified heterotic string theory represent largely degenerate classes of states in the quantum theory. We propose a simple expression for the full non--perturbative degeneracy, which contains no free continuous parameters and reproduces the Bekenstein-Hawking $S={A\over 4G_N}$ in the large-area limit (with the ${1\over 4}$ arising from microphysics). We sketch the elements of a physical picture leading to this expression: the holes support much hair, such that in counting it we are led to an effective string theory, and a matching condition whose solutions give the degeneracy.