Introduction: During recent years magnetosheath plasma structures called “jets” are identified in spacecraft data as localized regions in the magnetosheath where the dynamic pressure is enhanced compared to the background. Although the nomenclature and detection algorithms vary from author to author, magnetosheath jets are part of a larger class of phenomena which can be globally called magnetosheath irregularities. In this review we focus on elements of jets phenomenology less discussed in the literature, though sustained by theoretical models for solar wind magnetosphere interaction, numerical studies based on Vlasov equilibrium models or kinetic numerical simulations. Methods: The self-consistency of magnetosheath jets and the preservation of their physical identity (shape and physical properties), implicitly assumed in many recent experimental studies, is discussed in modelling and simulations studies and results as a consequence of kinetic processes at the edges of the jets. These studies provide evidence for the fundamental role played by a polarization electric field sustaining the forward motion of the jet with respect to the background plasma. Another natural consequence is the backward motion of surrounding magnetosheath plasma at the edges of jets. The conservation of magnetic moment of ions leads to a decrease of jets forward speed when it moves into increasing magnetic field. Our review is complemented by an analysis of magnetosheath data recorded by Cluster in 2007 and 2008. We applied an algorithm to detect jets based on searching localized enhancements of the dynamic pressure. Results: This algorithm identifies a number of 960 magnetosheath jets (354 events in 2007 versus 606 events in 2008). A statistical analysis of jet plasma properties reveals an asymmetric distribution of the number of jets as well as a dawn-dusk asymmetry of jets temperature and density. The perturbative effects of jets on the background magnetosheath density/temperature are stronger in the dusk/dawn flank. We also found evidence for deceleration and perpendicular heating of jets with decreasing distance to the Earth. The braking of jets is correlated with the variation of the magnetic field intensity: the stronger the magnetic field gradient, the more efficient is the jet breaking.