High-entropy alloys (HEAs) have drawn substantial attention on account of their outstanding properties. Additive manufacturing (AM), which has emerged as a successful approach for fabricating metallic materials, allows for the production of complex components based on three-dimensional (3D) computer-aided design (CAD) models. This paper reviews the advancements in the AM of HEAs, encompassing a variety of AM techniques, including selective laser melting (SLM), selective laser sintering (SLS), selective electron beam melting (SEBM), directed energy deposition (DED), binder jetting (BJT), direct ink writing (DIW), and additive friction stir deposition (AFSD). Additionally, the study discusses the powders and wires utilized in AM, the post-processing of AM-processed HEAs, as well as the mechanical and corrosion properties of these alloys. The unique ultra-fine and non-equilibrium microstructures achieved through AM result in superior mechanical properties of HEAs, like improved strength and ductility. However, research regarding certain aspects of HEA AM, such as fatigue properties and creep deformation behavior, is still relatively scarce. Future research should focus on overcoming the existing limitations and exploring the potential of HEAs in various applications.