The recognition in the 1990s that light beams with a helical phase front have orbital angular momentum has benefited applications ranging from optical manipulation to quantum information processing. Recently, attention has been directed towards the opportunities for harnessing such beams in communications. Here, we demonstrate that four light beams with different values of orbital angular momentum and encoded with 42.8 × 4 Gbit s-1 quadrature amplitude modulation (16-QAM) signals can be multiplexed and demultiplexed, allowing a 1.37 Tbit s-1 aggregated rate and 25.6 bit s-1 Hz-1 spectral efficiency when combined with polarization multiplexing. Moreover, we show scalability in the spatial domain using two groups of concentric rings of eight polarization-multiplexed 20 × 4 Gbit s-1 16-QAM-carrying orbital angular momentum beams, achieving a capacity of 2.56 Tbit s-1 and spectral efficiency of 95.7 bit s-1 Hz-1 . We also report data exchange between orbital angular momentum beams encoded with 100 Gbit s-1 differential quadrature phase-shift keying signals. These demonstrations suggest that orbital angular momentum could be a useful degree of freedom for increasing the capacity of free-space communications.