This paper addresses the scientific and technological challenges related to the development of wireless radio frequency (RF) coils for magnetic resonance imaging (MRI) based on published literature together with the authors' interpretation and further considerations. Key requirements and possible strategies for the wireless implementation of three important subsystems, namely the MR receive signal chain, control signaling, and on-coil power supply, are presented and discussed. For RF signals of modern MRI setups (e.g., 3 T, 64 RF receive channels), with on-coil digitization and advanced methods for dynamic range (DR ≥ 16-bit) and data rate compression, still data rates > 500 Mbps will be required. For wireless high-speed MR data transmission, 60 GHz WiGig and optical wireless communication appear to be suitable strategies; however, on-coil functionality during MRI scans remains to be verified. Besides RF signals, control signals for on-coil components, e.g., active detuning, synchronization to the MR system, and B 0 shimming, have to be managed. Wireless power supply becomes an important issue, especially with a large amount of additional on-coil components. Wireless power transfer systems (>10 W) seem to be an attractive solution compared to bulky MR-compatible batteries and energy harvesting with low power output. In our opinion, completely wireless RF coils will ultimately become feasible in the future by combining efficient available strategies from recent scientific advances and novel research. Besides ongoing improvement of all three subsystems, innovations are specifically required regarding wireless technologies, MR compatibility, and wireless power supply.