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Beams carrying orbital-angular-momentum (OAM) have gained much interest due to their unique amplitude and phase structures. In terms of communication systems, each of the multiple independent data-carrying beams can have a different OAM value and be orthogonal to all other beams. This paper will describe the use of multiplexing and the simultaneous transmission of multiple OAM beams for enhancing the capacity of communication systems. We will highlight the key advances and technical challenges in the areas of (a) free-space and fiber communication links,(b) mitigation of modal coupling and channel crosstalk effects,(c) classical and quantum systems, and (d) optical and radio frequency beam multiplexing.