There are many technical applications in the field of lightweight construction as, for example, in aerospace engineering, where stress concentration phenomena play an important role in the design of layered structural elements (so-called laminates) consisting of plies of fiber reinforced plastics or other materials. A well known stress concentration problem rich in research tradition is the so-called free-edge effect. Mainly explained by the mismatch of the elastic material properties between two adjacent dissimilar laminate layers, the free-edge effect is characterized by the concentrated occurrence of three-dimensional and singular stress fields at the free edges in the interfaces between two layers of composite laminates. In the present contribution, a survey on relevant literature from more than three decades of scientific research on free-edge effects is given. The cited references date back to 1967 and deal with approximate closed-form analyses, as well as numerical investigations by the finite element method, the finite difference method, and several other numerical techniques. The progress in research on the stress singularities which arise is also reviewed, and references on experimental investigations are cited. Related problems are also briefly addressed. The paper closes with concluding remarks and an outlook on future investigations. In all, 292 references are included.