Additive manufacturing (AM) technologies enable the fabrication of complex and customized structures with improved mechanical performance compared to conventional manufacturing. In particular, continuous fiber fused filament fabrication (CF4) can produce high-performance fiber-reinforced polymer composites by precisely controlling fiber orientation and placement. Furthermore, AM provides excellent design freedom that can be exploited using topology optimization (TO) to tailor structural performance. Various TO strategies have been proposed to design lightweight, high-performance structures, exploiting AM capabilities. This paper reviews works on TO strategies to obtain optimal fiber-reinforced composite (FRC) structures focusing on: (1) parameterization schemes to incorporate material anisotropy; (2) simultaneous and sequential approaches to optimize FRC distribution and orientation; (3) Multi-scale TO methods; (4) Emerging TO methodologies. The similarities, differences, challenges and outlook are discussed to provide directions for future research on exploiting AM capabilities through TO for performance enhancement.