Analysis of the shapes of diffraction peak profiles (DPPA) is a widely used method for characterising the microstructure of crystalline materials. The DPPA method can be used to determine details about a sample that include, the micro-strain, crystal size or dislocation cell size, dislocation density and arrangement, quantity of planar faults and dislocation slip system population.The main aim of this thesis is to evaluate the use of DPPA in studying the deformation of metals. The alloys studied are uni-axially deformed samples of nickel alloy, nickel-200, 304 and 316 stainless steel alloys and titanium alloys, Ti-6Al-4V and grade 2 CP-titanium.A number of DPPA methods were applied to these metals: a full-width method; a method that attributes size and strain broadening to the Lorentzian and Gaussian integral breadth of a Voigt; different forms of the variance method; the Williamson-Hall method; the alternative method; and variations of the Warren-Averbach method. It is found that in general the parameters calculated using the different methods qualitatively agree with the expectations and differences in the deformation of the different metals. For example, the dislocation density values found for all metals, are approximately the same as would be expected from TEM results on similar alloys. However, the meaning of the results are ambiguous, which makes it difficult to use them to characterise a metal. The most useful value that can be used to describe the state of a metal is the full-width. For a more detailed analysis the Warren-Averbach method in a particular form, the log format fitted to individual Fourier coefficients, is the most useful method.It was found that the shape of different diffraction peaks change in different texture components. These changes were found to be different for the different metals. A method to calculate the shape of diffraction peaks, in different texture components, using a polycrystal plasticity models was investigated. It was found that for FCC metals, the use of a Taylor model was able to qualitatively predict the changes in the shape of diffraction peaks, measured in different texture components. Whereas, for titanium alloys, a model which used the Schmid factor was able to qualitatively explain the changes. The differences in the FCC alloys was attributed to being due to differences in the stacking fault energy of the alloys. For nickel, which develops a heterogeneous cell structure, an additional term describing changes in the crystal size in different orientations is required. The differences between the titanium alloys were shown to be due the presence of twinning in CP-titanium and not in Ti-6Al-4V. This difference was thought to cause an additional broadening due to variations in intergranular strains in twinned and non-twinned regions. The use of polycrystal plasticity models, to explain the shape of diffraction peaks, raises questions as to the validity of some of the fundamental assumptions made in the use of most DPPA methods.