Existing rigorous theories of prediction of macroscopic elastic behavior of random media are discussed. Attention is focused on statistically homogeneous and isotropic multiphase materials and polycrystals and on fiber reinforced materials. Direct approaches for dilute suspensiontheory and variational approaches for arbitrary phase fractional volumes are surveyed. New results are given for elastic behavior of cubic polycrystalline mixtures and for a couple stress constant of a dilute spheres suspension.