Terahertz (THz)-band communications are celebrated as a key enabling technology for next-generation wireless systems that promises to integrate a wide range of data-demanding and delay-sensitive applications. Following recent advancements in optical, electronic, and plasmonic transceiver design, integrated, adaptive, and efficient THz systems are no longer far-fetched. In this article, we present a progressive vision of how the traditional "THz gap" will transform into a "THz rush" over the next few years. We posit that the breakthrough the THz band will introduce will not be solely driven by achievable high data rates, but more profoundly by the interaction between THz sensing, imaging, and localization applications. We first detail the peculiarities of each of these applications at the THz band. Then we illustrate how their coalescence results in enhanced environment-aware system performance in beyond-5G use cases. We further discuss the implementation aspects of this merging of applications in the context of shared and dedicated resource allocation, highlighting the role of machine learning.