Recent developments in additive manufacturing techniques have facilitated the fabrication of fiber-reinforced composite materials. In this paper, the mechanical properties and deformation mechanisms of discontinuous and continuous fiber-reinforced composites fabricated by various additive manufacturing techniques are comprehensively reviewed. The effects of fiber type, orientation and weight/volume fraction, printing path, and stacking sequence on the mechanical properties of additively manufactured composites are discussed. In addition, the applications of additively manufactured composites, the main challenges of the current additive manufacturing techniques, and recommendations for future work are also presented.