There have been substantial technical and policy discussions about the spectrum needs of 5G and the necessity of expanding access to higher frequency spectrum, including in the millimeter wave (mmWave) bands from 30 to 300 GHz. The focus, however, has been on bands below 60GHz, or at most 90GHz, which is the current limit of near-future commercial technologies. As wireless markets continue to grow, demand may arise for spectrum in still higher frequency bands above 90GHz, including in the sub-millimeter or Terahertz (THz) bands between 300GHz and 3THz. Although exploiting THz bands is at the frontiers of technical research today and the commercial case for it will depend on further demonstration of the value and constraints, it is worthwhile exploring how THz spectrum might impact wireless network architectures, business/usage cases, and spectrum policy. In this paper, we explore those challenges. We first explain some of the critical features of THz spectrum that make it both attractive and challenging to use and summarize the current state of our ability to address those challenges by reference to the current engineering research and commercialization progress on exploiting mmWave and higher frequencies. For example, the THz spectrum would offer virtually unbounded capacity (relative to today's demand forecasts) for supporting wide-channels and extremely high data rates, but with demanding Line of Sight (LOS) requirements. THz devices operate in very narrow beams, close to optical wavelengths, and have very limited capability to penetrate materials (e.g., even a sheet of paper is sufficient to block it). Integrating such spectrum into wireless networks will impose important requirements for antenna siting (small cell architectures) and backhaul, posing greater challenges for extending core-network services to edge-networks. We hypothesize that such spectrum may further empower equipment-based, end-user deployed strategies for deploying wireless networking, with interesting implications for industry structure and regulatory policy. Furthermore, because current spectrum policies are limited to radio frequencies below 300GHz (arguably below 90GHz), THz is the green-field frontier for spectrum policy-making. This offers an opportunity for novel thinking about how best to manage spectrum resources to enable efficient sharing. Moreover, shifting wireless services to THz might free up capacity in the currently scarce lower frequency bands (below 10GHz), with implications for how we should think about spectrum management across all frequency bands. This includes addressing the challenge of the appropriate licensing regime (e.g., exclusive or unlicensed) that should apply for the THz spectrum. A better understanding of the potential uses for the terahertz spectrum is essential for a better understanding of scarcity limits on the lower frequency spectrum. Although the focus of the analysis will be on the THz spectrum, informed by recent technical work being directed by the authors, the applicability of the insights will be more general and applicable to today's efforts to promote spectrum policy reform, wireless network regulation, and realization of the future beyond 5G applications that we are striving to implement.