Rydberg Atomic REceiver (RARE) is driving a paradigm shift in electromagnetic (EM) wave measurement by harnessing the electron transition phenomenon of Rydberg atoms. Operating at the quantum scale, such receivers have the potential to breakthrough the performance limit of classic receivers, sparking a revolution in physical-layer wireless communications. The objective of this paper is to offer insights into RARE-empowered communications. We first provide a comprehensive introduction to the fundamental principles of RAREs. Then, a thorough comparison between RAREs and classic receivers is conducted in terms of the antenna size, sensitivity, and bandwidth. Subsequently, we overview the recent progresses in RARE-aided wireless communications, covering the frequency-division multiplexing, multiple-input-multiple-output, wireless sensing, and quantum many-body techniques. Moreover, the unique application of RARE in multiband sensing and communication is introduced. Finally, we conclude by providing promising research directions.