The present-day trends and development prospects of stochastic averaging methods in composite mechanics are analyzed. The following methods are considered: the traditional one (the medium of comparison is homogeneous), the method of periodic components (the medium of comparison has a regular structure), the numerical method of local approximation with regard for the short-range order in the arrangement and interaction of inhomogeneities, and a synthesis of the periodic-component and local-approximation methods. A detailed procedure is presented for calculating the functionals of second, third, and higher orders of the stochastic problem. The results obtained are used for evaluating, in an explicit form, corrections to the effective elastic moduli found for quasi-isotropic and unidirectional fiber composites by the traditional averaging method and the method of periodic components. Analytical formulas for the second-order moment functions of structural stresses and strains are derived. It is shown that the fields of structural stresses and strains are locally ergodic. A new multilevel approach is proposed for designing composites, which takes into account the effect of structurally technological factors. Thus, unidirectional fiber composites are calculated by a two-level model, layered structures - by a three-level model, and carbon-carbon structures - by a five-level model. A stage-by-stage solution procedure is suggested for the boundary-value problem of micromechanics of composites. For a wide class of composites, the effective elastic moduli are calculated and the strength surfaces are constructed.