Structured electromagnetic (EM) waves carrying orbital angular momentum (OAM) have been explored in various frequency regimes to enhance the data capacity of communication systems by multiplexing multiple co-propagating orthogonal OAM beams (i.e., mode-division multiplexing (MDM)). Terahertz (THz) communications in free space have gained interest as THz waves tend to have: (a) larger bandwidth and lower beam divergence than millimeter-waves, and (b) lower interaction with matter conditions than optical waves. In this paper, we review recent experimental demonstrations of OAM-based THz MDM communication systems, including (i) THz MDM system with two multiplexed OAM beams; (ii) THz OAM multiplexing together with frequency-division-multiplexing (FDM) and polarization-division-multiplexing (PDM); (iii) multiplexing a full set of two-dimensional Laguerre-Gaussian (LG_(l,p)) beams; and (iv) THz integrated OAM emitter for OAM mode generation and multiplexing. System performance of THz OAM links with the effect of turbulence, divergence, and multipath is also simulated and analyzed.