In this paper, recent advances in the physics of low pressure inductively coupled plasmas (ICPs) are reviewed where the interaction of an electromagnetic field with electrons is governed by electron thermal motion rather than electron–atom collisions. Direct measurement of the rf electric field and rf current density in the plasma made it possible to distinguish between collisional and stochastic (collisionless) electron heating. Several new phenomena such as a wave phase bifurcation, phase velocity reversal, a second current layer and negative power absorption have been found and interpreted in terms of non-local electrodynamics. Nonlinear effects induced by the rf Lorentz force such as nonlinear plasma polarization and second harmonic currents, as well as modification of the spatial distribution of the plasma caused by ponderomotive forces have been demonstrated in ICP under discharge conditions typical for industrial applications.