Terahertz (THz)-band communications are currently being celebrated as a key technology that could fulfill the increasing demands for wireless data traffic in the upcoming sixth-generation (6G) of wireless communications. Many challenges, such as high propagation losses and power limitations, which result in short communication distances, have yet to be addressed for this technology to be realized. Ultra-massive multiple-input, multiple-output (UM-MIMO) antenna systems have emerged as practical means for combatting this distance problem, thereby increasing system capacity. Towards that end, graphene-based nano-antennas have recently been proposed, as they can be individually tuned and collectively controlled in compact UM-MIMO array-of-sub-arrays architectures. In this paper, we present a holistic overview of THz UM-MIMO systems. We assess recent advancements in transceiver design and channel modeling, and discuss the major challenges and shortcomings of such designs by deriving the relationship between communication range, array dimensions, and system performance. We further highlight several research advances that could enhance resource allocation at the THz band, including waveform designs, multi-carrier configurations, and spatial modulations. Based on this discussion, we highlight prospective use cases that can bring THz UM-MIMO into reality in the context of sensing, data centers, cell-free systems, and mid-range wireless communications.