Terahertz (THz) wireless communications have attracted interest due to the larger bandwidth and lower beam divergence than millimeter waves. THz waves also have lower interaction with matter conditions than optical waves. Furthermore, mode-division multiplexing can be used to increase the data capacity and spectral efficiency. The ability to multiplex multiple co-propagating beams is due to their orthogonality. One form of such structured beams is orbital angular momentum beams. In this paper, we review recent experimental demonstrations of OAM-based THz MDM communication systems when multiplexing two (i) OAM beams, (ii) OAM beams combined with frequency-division-multiplexing, and polarization-division-multiplexing, (iii) Laguerre-Gaussian modes by varying two spatial modal indices, and (iv) OAM beams using a THz integrated OAM emitter.