A number of techniques are presented for extrapolating from knowledge of the direct correlation function for a uniform fluid at various densities to that of the free energy and associated density profile of a nonuniform fluid. A primitive mathematical model is followed by models based upon physical characteristics of exactly solved systems, from the nonnegativity of linear response functions to the explicit form of a nonuniform hard rod fluid. Attention is paid to physical requirements which are not satisfied and suggestions are made for future progress.