Alloys with excellent properties are always in significant demand for meeting the severe conditions of industrial applications. However, the design strategies of traditional alloys based on a single principal element have reached their limits in terms of property optimization. The concept of high-entropy alloys (HEAs) provides a new design strategy based on multicomponent elements, which may overcome the bottleneck problems that exist in traditional alloys. To further maximize the capability of HEAs, a novel additive manufacturing (AM) technique has been utilized to produce HEA components with the desired structures and properties. This review considers a new trend in the AM of HEAs, i.e., from the AM of single-phase HEAs to multiphase HEAs. Although most as-printed single-phase HEAs show superior tensile properties to as-cast ones, their strength is still not satisfactory, especially at elevated temperatures. Thus, multiphase HEAs are developed by introducing hard second phases, such as L12, BCC, carbides, oxides, nitrides, and so on. These phases can be introduced to the matrix using in situ alloying during AM or the subsequent heat treatment. Dislocation strengthening is considered as the main reason for improving the tensile properties of as-printed single-phase HEAs. In contrast, multiple strengthening and toughening mechanisms occur in as-printed multiphase HEAs, which can synergistically enhance their mechanical properties. Furthermore, machine learning provides an effective method to design new alloys with the desired properties and predict the optimal AM parameters for the designed alloys without tedious experiments. The synergistic combination of machine learning and AM will significantly speed up scientific advances and promote industrial applications.