The advancement of Rydberg Atomic REceiver (RARE) is driving a paradigm shift in electromagnetic (EM) wave measurement. RAREs utilize the electron transition phenomenon of highly-excited atoms to interact with EM waves, thereby enabling wireless signal detection. Operating at the quantum scale, such new receivers have the potential to breakthrough the sensitivity limit of classical receivers, sparking a revolution in physical-layer wireless communications. The objective of this paper is to offer insights into RARE-aided communication systems. We first provide a comprehensive introduction to the fundamental principles of RAREs. Then, a thorough comparison between RAREs and classical receivers is conducted in terms of the antenna size, sensitivity, coverage, and bandwidth. Subsequently, we overview the state-of-the-art design in RARE-aided wireless communications, exploring the latest progresses in frequency-division multiplexing, multiple-input-multiple-output, wireless sensing, and quantum many-body techniques. Finally, we highlight several wireless-communication related open problems as important research directions.