Bulk metallic glasses (BMGs) and high entropy alloys (HEAs) are both important multi-component alloys with novel microstructures and unique properties, which make them promising for applications in many industries. However, certain hindrances have been identified in the fabrication of BMGs and HEAs by conventional techniques due to the intrinsic requirements of BMGs and HEAs. With the advent of metal additive manufacturing, new opportunities have been perceived to fabricate geometrically complex BMGs and HEAs with tailorable microstructure theoretically at any site within the specimen, which are not achievable using conventional fabrication techniques. After providing some background and introducing the conventional fabrication techniques for BMGs and HEAs, this review will focus on the current status, development, and challenges in metal additive manufacturing of BMGs and HEAs including different additive manufacturing techniques being used, microstructure design and evolution, as well as properties of the fabricated BMGs and HEAs. A future outlook of metal additive manufacturing of BMGs and HEAs will also be provided at the end.