In the present article we survey papers on edge effects investigated by the rigorous approach. We interpret edge effects as stressed states created in a composite as a result of zones in which the stresses exhibit a rapidly changing behavior in comparison with the slow variation of the stresses outside such zones. Here the range of the edge effect is defined as the distance from the point of its inception to the boundary of the edge zone in a given direction. The transition of the stresses to the slowly varying state is determined within prescribed error limits. The size and configuration of the edge zone depends on the tolerated error. Clearly, the main difficulty associated with the rigorous approach is finding solutions of the elasticity problems. The finite-difference approach is suggested for the approximate solution of these problems. In light of the comparative time consumption of the finite-difference approach, it is best directed at certain classes of problems rather than at particular individual problems. Not too many papers on the investigation of edge effects by the rigorous approach have been published to date. Below, following in their footsteps, we formulate edge effect problems in composites, determine classes of problems, andmore » investigate edge effects in composite materials and structural elements using them in Cartesian (planar and three-dimensional problems) and cylindrical (axisymmetric problems) coordinate frames. We note that the division of approaches to the study of edge effects into qualitative (nonrigorous) and quantitative (rigorous) reflects the authors own point of view. Of course, other schemes of classification of the approaches to the investigation of the regions of rapidly varying states in composites are possible.« less