Terahertz (THz) band communications is envisioned as a key technology for future wireless standards. Advances in hardware design, channel models, and signal processing have all contributed significantly to advancing the field. Practical THz wireless has been demonstrated in high data-rate backhaul links. However, the next great leap for adopting THz-band frequencies in widespread communication systems must cover a massive canyon. Such communication systems must operate in the massive near field of the high-gain devices that are required to overcome the very high spreading losses of THz frequencies while providing all the promises of very high data rates and sensing resolution. Recent years have seen progress toward near-field THz, with investigations centered around the physical layer, combining both wave and communication theory to provide meaningful solutions to the challenges of THz signal propagation in the near field. In this article, an in-depth look is presented on the aspect of near-field THz. The aspect of signal propagation is first explained from a symbiosis of array and wave theory, following which it is conclusively shown how canonical beamforming is decimated in the near field. It is further explained why THz wireless must necessarily be near field, at least in some cases. Then, a vision of beamshaping is presented in which wavefront engineering is presented to address the design of new beams, specifically beamfocusing, Bessel beams, and Airy beams, which each offer distinct attractive advantages in creating THz links. Issues related to their generation and reception and issues involving narrowband limitations are presented. Finally, the article ends by discussing some of the more promising and upcoming applications of these beams as well as the exciting challenges and opportunities in this new and intriguing research area.