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Late visions and trends for the future sixth Generation (6G) of wireless communications advocate, among other technologies, towards the deployment of network nodes with extreme numbers of antennas and up to terahertz frequencies, as means to enable various immersive applications. However, these technologies impose several challenges in the design of radio-frequency front-ends and beamforming architectures, as well as of ultra-wideband waveforms and computationally efficient transceiver signal processing. In this article, we revisit the Time Reversal (TR) technique, which was initially experimented in acoustics, in the context of large-bandwidth 6G wireless communications, capitalizing on its high resolution spatiotemporal focusing realized with low complexity transceivers. We first overview representative state-of-the-art in TR-based wireless communications, identifying the key competencies and requirements of TR for efficient operation. Recent and novel experimental setups and results for the spatiotemporal focusing capability of TR at the carrier frequencies $2.5$, $36$, and $273$ GHz are then presented, demonstrating in quantitative ways the technique's effectiveness in these very different frequency bands, as well as the roles of the available bandwidth and the number of transmit antennas. We also showcase the TR potential for realizing low complexity multi-user communications. The opportunities arising from TR-based wireless communications as well as the challenges for finding their place in 6G networks, also in conjunction with other complementary candidate technologies, are highlighted.