Plasma flows with enhanced dynamic pressure, known as magnetosheath jets, are often found downstream of collisionless shocks. As they propagate through the magnetosheath, they interact with the surrounding plasma, shaping its properties, and potentially becoming geoeffective upon reaching the magnetopause. In recent years (since 2016), new research has produced vital results that have significantly enhanced our understanding on many aspects of jets. In this review, we summarise and discuss these findings. Spacecraft and ground-based observations, as well as global and local simulations, have contributed greatly to our understanding of the causes and effects of magnetosheath jets. First, we discuss recent findings on jet occurrence and formation, including in other planetary environments. New insights into jet properties and evolution are then examined using observations and simulations. Finally, we review the impact of jets upon interaction with the magnetopause and subsequent consequences for the magnetosphere-ionosphere system. We conclude with an outlook and assessment on future challenges. This includes an overview on future space missions that may prove crucial in tackling the outstanding open questions on jets in the terrestrial magnetosheath as well as other planetary and shock environments.