The compound Bi₂Sr₂CaCu₂O_8+δ is of special interest for two reasons: it is an important member of the family of cuprates who possess superconducting transitions at high temperatures, and it is an example of the class of layered compounds whose structures are distinguished by incommensurate modulation. The unique normal state and superconducting properties of the cuprates are intricately linked to their far from ideal disordered structures. The additional incommensurate nature of some compounds has greatly hampered the understanding of their novel behaviour. This thesis describes single crystal studies of Bi₂Sr₂CaCu₂O_8+δ using x-ray scattering techniques as a tool for establishing in detail those structural features of significance to the behaviour of this compound as a superconductor, and those of importance to its nature as an incommensurate. The thesis starts with the characterisation of the variations between crystals grown, using flux and floating zone methods, by four separate research groups. The inclusion of impurities is found to be a feature of flux grown crystals. The nature of the incommensurate modulation is also clarified, and defects associated with it are identified. The fundamental properties of the modulation are investigated by studying in situ the response of the structure to high temperature. It is demonstrated that the modulation is strongly pinned and that the incommensurate period of the modulation is not a continuous function of oxygen content; a possible oxygen deficient high temperature phase is tentatively identified. The inert nature of the incommensurability to temperature is also established at low temperature, down to 20K, limiting any possible direct involvement of the modulation in the superconducting transition. Oxygen content, on the other hand, is known to hold a major influence over both normal state and superconducting properties, and a study is made of the effects of nitrogen and oxygen annealing treatments. The results reveal modifications in microstructure associated with oxygen ordering, a result of potential importance to the understanding of transport properties.