A review is given of the techniques associated with low-temperature thermal equilibrium nuclear orientation, detected using nuclear radiations. Following an introductory section that includes a historical summary, a brief description of the formalism and of some experimental aspects of nuclear orientation is presented. Various applications of nuclear orientation are then treated in detail, with emphasis on recent developments and new experiments in the field. The applications are grouped, according to the particular experimental techniques used, into static orientation, nuclear resonance methods, and time-dependent methods.