This is the second part of a set of two papers on radio-frequency (RF) discharges, part of a larger series on the foundations of plasma and discharge physics. In the first paper (Chabert et al 2021 Plasma Sources Sci. Technol. 30 024001) the two basic configurations of RF discharges commonly used in industrial applications, the capacitive and the inductive discharges, are presented. The introduction of an external magnetic field to these discharges results in not only a quantitative enhancement of their capabilities but also leads to qualitatively different interaction mechanisms between the RF field and the plasma. This provides rich opportunities for sustaining dense plasmas with high degrees of ionization. On one hand, the magnetic field influences significantly the particle and energy transport, thus providing new possibilities for control and adjustment of the plasma parameters and opening even lower operation pressure windows. On the other hand, when the magnetic field is introduced also in the region where the plasma interacts with the RF field, qualitatively new phenomena arise, that fundamentally change the mechanisms of power coupling to the plasma—the electromagnetic energy can be transported as waves deeper into the plasma volume and/or collisionlessly absorbed there by wave resonances. The characteristics of these discharges are then substantially different from the ones of the standard non-magnetized RF discharges. This paper introduces the physical phenomena needed for understanding these plasmas, as well as presents the discharge configurations most commonly used in applications and research. Firstly, the transport of particles and energy as well as the theory of waves in magnetized plasmas are briefly presented together with some applications for diagnostic purposes. Based on that the leading principles of RF heating in a magnetic field are introduced. The operation and the applications of various discharges using these principles (RF magnetron, helicon, electron cyclotron resonance and neutral loop discharges) are presented. The influence of a static magnetic field on standard capacitive and inductive discharges is also briefly presented and discussed.