The fifth-generation (5G) wireless network is coming for expected extremely high data-rate, capacity and connectivity for mobile applications. In the new network, antenna technology has been one of the key challenges for conventional antenna R&D. On the other hand, metamaterials or metasurfaces as new electromagnetic phenomena have been one of the hottest research topics in the electromagnetic community, in particular, antenna engineering. Starting with the new requirements for 5G antennas, the important changes in antenna engineering are introduced and then the concepts of metamaterials, in particular, metasurfaces are briefed. After that, the recent progress in the research and development of millimeter-wave/microwave metasurface antennas (metantennas in short) is updated with design examples.