A review is made of investigations of the mechanics of curved composites. By curved composites we mean unidirectional fibrous and layered composites whose reinforcing fibers or layers have an initial curving or bending. The investigations carried out Within the framework of the continuum theories and within the framework of the piecewise-homogeneous body model are considered separately. The corresponding theories, formulation of the problems, and solution methods for these problems are considered and some typical results on the influence of the curvature on the mechanical behavior of the composite are analyzed. Subjects for future investigations are presented.