Abstract Plasma jets are sources of repetitive and stable ionization waves, meant for applications where they interact with surfaces of different characteristics. As such, plasma jets provide an ideal testbed for the study of transient reproducible streamer discharge dynamics, particularly in inhomogeneous gaseous mixtures, and of plasma–surface interactions. This topical review addresses the physics of plasma jets and their interactions with surfaces through a pedagogical approach. The state-of-the-art of numerical models and diagnostic techniques to describe helium jets is presented, along with the benchmarking of different experimental measurements in literature and recent efforts for direct comparisons between simulations and measurements. This exposure is focussed on the most fundamental physical quantities determining discharge dynamics, such as the electric field, the mean electron energy and the electron number density, as well as the charging of targets. The physics of plasma jets is described for jet systems of increasing complexity, showing the effect of the different components (tube, electrodes, gas mixing in the plume, target) of the jet system on discharge dynamics. Focussing on coaxial helium kHz plasma jets powered by rectangular pulses of applied voltage, physical phenomena imposed by different targets on the discharge, such as discharge acceleration, surface spreading, the return stroke and the charge relaxation event, are explained and reviewed. Finally, open questions and perspectives for the physics of plasma jets and interactions with surfaces are outlined.