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This article summarizes the recently discovered opportunities of geodesic lenses for producing high-performing antennas for 5G/6G communications. First, we explain the operation of these lenses based on Geometrical Optics with rays that follow “the shortest optical path” on the geodesic surface. Also, we explain the connection between geodesic lenses and rotationally symmetric graded-index lenses. Generally, geodesic lenses can be implemented without the need of dielectric materials, resulting in very efficient devices constructed with a fully-metallic configuration. When combined with a feeding network and a radiating transition, such as a flare or a leaky wave, they can produce a multiple-beam lens antenna, of interest for applications requiring one-dimensional (e.g., azimuthal) coverage diversity such as in cell tower communication systems. Prototypes of these antennas have been recently tested, demonstrating remarkable performance in the Ka-band, part of which is considered for 5G. At high operational frequencies allocated for 5G/6G, geodesic lenses offer an opportunity to produce cost-effective antenna solutions with high directivity, high efficiency and spatial diversity through multiple beams. [ABSTRACT FROM AUTHOR]