Purpose Advanced fibre-reinforced polymer (FRP) composites have been increasingly used over the past two decades for strengthening, upgrading and restoring degraded civil engineering infrastructure. Substantial experimental investigations have been conducted in recent years to understand the compressive behaviour of FRP-confined concrete columns. A considerable number of confinement models to predict the compressive behaviour of FRP-strengthened concrete columns have been developed from the results of these experimental investigations. The purpose of this paper is to present a comprehensive review of experimental investigations and theoretical models of circular and non-circular concrete columns confined with FRP reinforcement. Design/methodology/approach The paper reviews previous experimental test results on circular and non-circular concrete columns confined with FRP reinforcement under concentric and eccentric loading conditions and highlights the behaviour and mechanics of FRP confinement in these columns. The paper also reviews existing confinement models for concrete columns confined with FRP composites in both circular and non-circular sections. Findings This paper demonstrates that the performance and effectiveness of FRP confinement in concrete columns have been extensively investigated and proven effective in enhancing the structural performance and ductility of strengthened columns. The strength and ductility enhancement depend on the number of FRP layers, concrete compressive strength, corner radius for non-circular columns and intensity of load eccentricity for eccentrically loaded columns. The impact of existing theoretical models and directions for future research are also presented. Originality/value Potential researchers will gain insight into existing experimental and theoretical studies and future research directions.