The Rydberg atomic quantum receivers (RAQR) are emerging quantum precision sensing platforms designed for receiving radio frequency (RF) signals. It relies on creation of Rydberg atoms from normal atoms by exciting one or more electrons to a very high energy level, thereby making the atom sensitive to RF signals. RAQRs realize RF-to-optical conversions based on light-atom interactions relying on the so called electromagnetically induced transparency (EIT) and Aulter-Townes splitting (ATS), so that the desired RF signal can be read out optically. The large dipole moments of Rydberg atoms associated with rich choices of Rydberg states and various modulation schemes facilitate an ultra-high sensitivity ($\sim$ nV/cm/$\sqrt{\text{Hz}}$) and an ultra-broadband tunability (direct-current to Terahertz). RAQRs also exhibit compelling scalability and lend themselves to the construction of innovative, compact receivers. Initial experimental studies have demonstrated their capabilities in classical wireless communications and sensing. To fully harness their potential in a wide variety of applications, we commence by outlining the underlying fundamentals of Rydberg atoms, followed by the principles and schemes of RAQRs. Then, we overview the state-of-the-art studies from both physics and communication societies. Furthermore, we conceive Rydberg atomic quantum single-input single-output (RAQ-SISO) and multiple-input multiple-output (RAQ-MIMO) schemes for facilitating the integration of RAQRs with classical wireless systems. Finally, we conclude with a set of potent research directions.