Similar to reflectors, lenses can be used to increase the directivity of conventional antennas. The Luneburg lens is a convenient solution that permits multiple/steerable beams with no scan losses. This feature is desirable for antennas in both ground and satellite communications. Depending on the practical needs and physical constraints, Luneburg lenses can be implemented in three- and two-dimensional versions. In the case of three-dimensional lenses, the research has been recently focused in additive manufacturing, which can drastically reduce their cost of implementation. Differently, in two-dimensional versions, the research has been aimed at reducing the use of dielectrics, so losses are reduced, specially in the millimetre wave band. In this contribution, we discuss some relevant implementations of Luneburg lens antennas, and we summarize their use for communications systems.