The increasing demand for higher bandwidth and higher speed wireless communication motivates the exploration of higher frequency bands. The Terahertz (THz) band (0.06-10 THz) is envisioned as one of the key players to meet the demand for such higher bandwidth and data rates. However, the available bandwidth at THz frequencies comes with the cost of a much higher propagation loss. Due to the power limitations of compact solid-state THz transceivers, this results in very short communication distances of approximately one meter. In this paper, the concept of Ultra-Massive Multiple Input Multiple Output (UM MIMO) communication is introduced as a way to increase the communication distance and the achievable capacity of THz-band communication networks. The very small size of THz plasmonic nano-antennas, which leverage the properties of nanomaterials and metamaterials, enables the development of very large plasmonic arrays in very small footprints. For frequencies in the 0.06-1 THz range, metamaterials enable the design of plasmonic antenna arrays with hundreds of elements in a few square centimeters (e.g., 144 elements in 1 cm 2 at 60 GHz). In the 1 to 10 THz band, graphene-based plasmonic nano-antenna arrays with thousands of elements can be embedded in a few square millimeters (e.g., 1024 elements in 1 mm 2 at 1 THz). The resulting arrays can be utilized both in transmission and in reception (e.g., 1024x1024 UM MIMO at 1 THz) to support di↵erent modes, from razor-sharp UM beamforming to UM spatial multiplexing, as well as multi-band communication schemes. After introducing the main properties of plasmonic nano-antenna arrays, the working modes of UM MIMO are presented, and preliminary results are provided to highlight the potential of this paradigm. Finally, open challenges and potential solutions to enable UM MIMO communication are described.