The mathematical theory of orthogonal polynomials and continued fractions provides efficient tools, via the recursion and related methods, for calculating diagonal elements of Green's function of tight-binding Hamiltonians. We present two recent generalizations of this formalism. The first one allows the calculation of conductivity and other linear response coefficients. The second one provides a new approach to the solution of mean-field theories of alloys. In particular it is shown that the self-consistent CPA equations can be easily solved, through a real-space calculation, for multi-component alloys based on periodic or non periodic lattices.