High-power terahertz (THz) radiation is fundamental to numerous applications in many fields. Ultraintense laser-produced plasmas have attracted ever-increasing interest as a damage-free medium for generating high-peak-power THz pulses. This article gives the authors' perspectives on how the field of ultraintense laser-driven THz radiation from plasmas developed and where the field is headed. In particular, recent advances and some new ideas are outlined in terms of THz genesis, metrology, and applications. In addition to pushing the limits of achievable THz pulse energies and peak powers, much attention will be paid on the tunability of THz properties. Single-shot THz metrology will develop toward multi-dimensional resolution. The resulting extreme THz radiation offers immense opportunities in the THz control over matter and THz-driven strong-field physics. A selection of illustrative application cases in the field of materials, chemistry, and biology are briefly discussed. In the authors' opinion, the concerted advances in these aspects will propel this field into the bright future.