Multicomponent high- and medium-entropy alloys (HEAs & MEAs) composed of multiple principal elements have attracted great interest owing to their considerable potentials for achieving unprecedented properties in their practically infinite compositional space. Apart from exceptional mechanical properties such as high strength and good ductility, it has been shown that excellent magnetic, electrical and thermal properties can also be involved in HEAs & MEAs via compositional and microstructural design. In this talk, we will present the unique combinations of multiple functions and even mutually exclusive properties that we have successfully achieved in recently developed multicomponent HEAs/MEAs. The multiple functions include high strength, good ductility, electrical resistivity, soft magnetism, low thermal expansion (Invar), resistance to corrosion and hydrogen embrittlement. The associated design strategies will be clarified and some potential directions for further developing multifunctional HEAs/MEAs will also be briefly discussed.