Abstract This paper is the first from a set of two companion papers on radio-frequency (RF) discharges. These two papers are in turn part of a larger series on the foundations of plasma and discharge physics. In this part we cover the basics of non-magnetized capacitive and inductive RF discharges, introduce the main concepts related to them and provide reference literature for further reading. In the second part we concentrate on RF discharges in the presence of external magnetic field. These types of RF discharges find a wide range of applications in various industries. Among the most prominent examples are the microelectronics industry for etching and deposition of thin films, the medical and food industry for the application of various coatings and changing the wettability of surfaces, the space industry to power ion-gridded thrusters for satellites, the fusion and elementary particle research for the production of beams of energetic ions or atoms. The paper introduces the basic concepts of RF power deposition and describes in more detail the operating conditions of the plasma reactors. The most important physical phenomena encountered in these discharges are outlined through the use of simplified models. The paper is intended as an entry point for newcomers to the field and provides ample of references (including textbooks) for further reading on the more specific and/or subtle aspects of the operation of these types of RF discharges.