Confinement with fiber‐reinforcement polymer (FRP) materials is a technique, which can increase adequately the axial strain ductility of concrete. Plain and reinforced concrete columns, with circular, square and rectangular cross sections, confined with FRP materials, subjected to monotonic or cyclic compressive load, have been extensively studied over the last 35 years. Also, a lot of predictive expressions for peak and ultimate axial strength and strain, suitable for the available concrete sections, have been proposed. However, it is proven that it is difficult to accurately model and predict the behavior of the noncircular confined concrete columns, especially in the presence of internal longitudinal and transverse steel reinforcement, which is the real case for the majority of existing reinforced concrete structures. The presented study gathers all the available test results on square and rectangular reinforced or plain concrete columns confined with FRP materials and other novel techniques, subjected only to cyclic axial loading. It also assesses the performance of four significant expressions published in literature for the prediction of column load and deformation, proposed for the peak and ultimate conditions.