The fifth-generation (5G) communication is currently under intensive research and development from both industry and academia. The new 5G cellular systems are envisioned to achieve better performance, e.g., higher data rate, better energy efficiency, and higher reliability than current systems. Nowadays, 5G commercialization has started in quite a few countries, and beyond 5G (B5G) and even some initial 6G research has already started. Antenna systems are critical components for 5G/B5G communication systems. Tremendous efforts have been exerted on researching 5G/B5G antenna systems and associated technologies. There are many 5G/B5G enabling antenna techniques, such as Massive MIMO array antennas in both conventional popular bands and millimeter-wave (mm-Wave) bands (with hundreds of antenna elements), terahertz (THz) antennas, antennas/arrays for inter-satellite and satellite-to-mobile communications, mm-Wave antennas/arrays for mobile terminals, antenna in package and device body including Front End Module and so on. These new antenna techniques, as well as mm-Wave antenna arrays without standard antenna ports, outdate the conventional antenna testing method. Furthermore, how to test the 5G antenna systems becomes a nontrivial task. Some efforts have also been exerted on efficient testing methodologies for 5G antenna systems. Yet there are still many challenges for cost-effective, repeatable, and accurate 5G antenna testing systems. Testing methodology for 5G/B5G antenna systems is still an open problem to date and, therefore, deserves full attention.