Wireless communication at the terahertz (THz) frequency bands (0.1-10THz) is viewed as one of the cornerstones of tomorrow's 6G wireless systems. Owing to the large amount of available bandwidth, THz frequencies can potentially provide wireless capacity performance gains and enable high-resolution sensing. However, operating a wireless system at the THz-band is limited by a highly uncertain channel. Effectively, these channel limitations lead to unreliable intermittent links as a result of a short communication range, and a high susceptibility to blockage and molecular absorption. Consequently, such impediments could disrupt the THz band's promise of high-rate communications and high-resolution sensing capabilities. In this context, this paper panoramically examines the steps needed to efficiently deploy and operate next-generation THz wireless systems that will synergistically support a fellowship of communication and sensing services. For this purpose, we first set the stage by describing the fundamentals of the THz frequency band. Based on these fundamentals, we characterize seven unique defining features of THz wireless systems: 1) Quasi-opticality of the band, 2) THz-tailored wireless architectures, 3) Synergy with lower frequency bands, 4) Joint sensing and communication systems, 5) PHY-layer procedures, 6) Spectrum access techniques, and 7) Real-time network optimization. These seven defining features allow us to shed light on how to re-engineer wireless systems as we know them today so as to make them ready to support THz bands. Furthermore, these features highlight how THz systems turn every communication challenge into a sensing opportunity. Ultimately, the goal of this article is to chart a forward-looking roadmap that exposes the necessary solutions and milestones for enabling THz frequencies to realize their potential as a game changer for next-generation wireless systems.