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Here, we explain the principles of operating lens antennas, and discuss their potential application for future 5G communications systems. We discuss the connection between the nomenclature employed in the optics and microwave communities, such as the direct relationship between aberrations and directivity and side lobe levels. Furthermore, we explain the potential of two innovative techniques: transformation optics and metasurfaces. Transformation optics, and specifically the concept of bespoke lenses, can be employed to make lenses ad hoc for specific feedings. Metasurfaces can be employed to produce two-dimensional low-cost lenses that can be fully metallic, which is an advantage in terms of losses. Finally, we introduce the concept of higher symmetries that can be used to increase the bandwidth of operation of these metasurfaces lenses.