Metamaterials are featured by artificial composite structures with exotic properties, which process promising application potentials in various areas. However, the manufacturing of metamaterials faces great challenges due to the structural complexity, accuracy requirement, and small scale. Additive manufacturing (AM), as a layer-by-layer technique, shows intrinsic advantages in the fabrication of metamaterials. This paper extensively reviews the current state on how and to what extent AM techniques are adopted for metamaterials fabrication, in which the metamaterials are mainly classified into mechanical, acoustic and electromagnetic types. More importantly, the challenges and research opportunities are discussed for AM fabrication of metamaterials, with focus on high precision, multi-structural and multi-material, topology optimization, support structure, anisotropy and heterogeneity, residual stresses and application realization. It is expected that with further innovative solutions being developed to bridge the research gaps, the industries will become more confident to adopt metamaterials in devices and systems for critical applications.