In the process of material innovation, multi-phase and composite materials have been developed to achieve high performance and reliability. Residual stresses inevitably introduced into materials often play a key role in performance and reliability. To measure residual stresses in crystalline materials, the X-ray diffraction method has been used as one of the most powerful nondestructive tools, and so has been the neutron diffraction method as a complimentary tool. Both X-ray and neutron methods are based on crystal diffraction. Diffractions from crystals are separately recorded depending on the crystalline structure, and the mean stress in each diffracting phase, called phase stress, is calculated from the peak shift of each separated diffraction profile. The macrostress is determined from phase stresses using the rule of mixture. The deviation of each phase stress from the macrostress is named microstress. In the present article, the fundamentals of measurements of phase stresses and the determination of macrostress and microstress are described. Micromechanics are briefly presented as a basis for theoretical analysis of phase stresses in composites. Applications of the X-ray and neutron methods to the measurement of residual macrostress and microstress in various multi-phase materials, metal-based, ceramic-based, polymer-based composites are reviewed, together with future perspective of the methods.