This paper gives a brief review of the Green's function method for solution of the general three-dimensional Boussinesq problem for advanced materials that are highly anisotropic. The Boussinesq problem refers to calculation of stress and/or strain fields in semi-infinite solids, subject to surface loading by solving the equations of elastostatic equilibrium. Analytical and semi-analytical expressions are derived for the elastostatic Green's functions based upon the delta-function representation developed earlier. The Green's function provides a computationally efficient method for solving the anisotropic Boussinesq problem. The Green's function should be useful for modeling physical systems of topical interest such as nanostructures in semiconductors, interpretation of nanoindentation measurements, and application to the boundary-element method of stress analysis of advanced materials. Numerical results for displacement and stress fields are presented for carbon-fiber composites having general orthotropic, tetrahedral, and hexagonal symmetries, and single-crystal silicon having cubic symmetry.