A micromechanics theory based on the analysis of a repeating cell in a fiber-reinforced material is reviewed. The analysis leads to the prediction of the overall behavior of various types of composites from the known material properties of fiber and matrix. The capability of the theory in providing the response of elastic, thermoelastic, viscoelastic, and viscoplastic composites, as well as their initial yield surfaces, strength envelopes, and fatigue failure curves, is demonstrated.