A detailed programme of methods for calculating and measuring crystal Bragg reflection characteristics is presented. The characterisation of an analyser involves determination of, as a function of wavelength, the Bragg dispersion function (defined in Chapter 2) and Rc, wc, Pc the integral, width and peak respectively of P lambda(theta) the crystal line spread function (or diffraction profile). Calculations are based on the Prins perfect lattice, Darwin zero-extinction and zero-absorption models,outlines of which are given. Measurement methods for determining the Bragg dispersion function and P lambda(theta) of an analyser are described. A comparison of various 1- and 2-reflection techniques used to measure RC(lambda) is made and from this it is clear that the chosen 2-reflection methods,with the inclusion of appropriate polarisation corrections,provide an efficient means of measuring this characteristic. Likewise a comparison is made of 1-, 2- and 3-reflection techniques previously used to determine P lambda(theta) and a new technique is introduced. This latter involves perturbing the calculated Prins function so that a fit between the self-convolution of the perturbed function and the (1,-1) rocking curve is obtained. Only perturbations which model the effects of known lattice defects are allowed. Within the limits discussed the perturbed function describes the true P lambda(theta). Emphasis is placed upon instrument alignment, and measurement conditions required,in all measurement techniques used. A description of the Leicester 2-crystal spectrometer and its alignment is included,together with measurement procedures. The above methods are applied in full characterisations of the analysers PET (002), EDdT (020) and ADP (101). Also included are calculated results for SHA (110) which allow interpretation of previous studies made by measurement alone. The thesis concludes with two brief reports of crystal calibration studies for the satellite UK5 and for American Science and Engineering. These reports illustrate the application of the methods used in this study to other research work.