In recent years, additive manufacturing techniques have been increasingly applied in the production of continuous fiber-reinforced composites (CFRCs). However, most advancements have focused on the fabrication of planar CFRC structures, whereas many engineering applications involve non-planar structures. Progress in 3D printing of non-planar CFRCs remains limited, representing an emerging cutting-edge area with significant potential for engineering applications. This review focuses on the state-of-the-art in non-planar 3D printing techniques for CFRC structures and elaborates their future perspectives and potential challenges. A comprehensive discussion is presented on the distinctions between non-planar and conventional planar 3D printing methods, and the materials and processes currently employed in these studies are critically examined. Three common methods of curved layer slice-path generation for CFRC structure are introduced. In addition, the article specifically addresses various non-planar printing approaches, including support-based techniques, such as threeaxis and multi-axis printing, as well as support-free methods relying on rapid cooling and photopolymerization processes. Finally, based on the challenges of non-planar printing techniques in path planning, manufacturing processes, and performance optimization, potential research directions for the future are outlined.