Theoretical and experimental advances in the techniques available for solving crystal structures have led to the development of several powerful techniques for solving complex structures, including those of proteins. Michael Woolfson and Fan Hai-fu describe all the available methods and how they are used. In addition to traditional methods such as the use of the Patterson function and isomorphous replacement, and the direct methods, the authors include methods that use anomalous scattering and observations from multiple-beam scattering. The fundamental physics and mathematical analyses are fully explained. Practical aspects of applying the methods are emphasised.