• The progress in additive manufacturing of ceramic matrix composites is reviewed systematically and comprehensively. • The benefits of additive manufacturing in fabricating ceramic matrix composites are provided. • The ceramic matrix composites include conventional second phase reinforcement composites and bioinspired composites. • The challenges of building ceramic matrix composites via additive manufacturing are analyzed. Additive manufacturing (AM) of ceramic matrix composites (CMCs) has enabled the production of highly customized, geometrically complex and functionalized parts with significantly improved properties and functionality, compared to single-phase ceramic components. It also opens up a new way to shape damage-tolerant ceramic composites with co-continuous phase reinforcement inspired by natural materials. Nowadays, a large variety of AM techniques has been successfully applied to fabricate CMCs, but variable properties have been obtained so far. This article provides a comprehensive review on the AM of ceramic matrix composites through a systematic evaluation of the capabilities and limitations of each AM technique, with an emphasis on reported results regarding the properties and potentials of AM manufactured ceramic matrix composites.