X-ray stress measurement is widely used as one of the most powerful nondestructive tools to measure residual stresses in polycrystalline solids. In most cases, the sin²Ψ method has been used to determine the stress. In recent years, however, the cosα method has attracted engineers as a new method to measure the stress using two-dimensional detectors, such as imaging plates. The present article is the review of the state of the art of the cosα method. For biaxial stress cases, the cosα method utilizes the whole Debye-Scherrer ring recorded on a two-dimensional detector taken by single exposure of X-rays, and normal and shear stresses are determined simultaneously. The accuracy of the stress measurement of the cosα method has been confirmed to be equivalent to that of the sin²Ψ method for various metals. The simple optical system of the cosα method makes stress analyzers smaller, lighter and more convenient to use for on-site or field measurements. A recent portable stress analyzer adopting the cosα method shortens the measurement time to 60 s. The method has been further developed to analyze triaxial residual stresses. Various advantages of the cosα method are highlighted in comparison with the other methods of X-ray stress determination. Applications of the cosα method to machines and engineering structures are presented, together with future perspectives of the method.