When the supersonic solar wind meets Earth's magnetosphere, a shock wave forms in space. Shocked plasma flows around the edges of the magnetopause in a hot, dense, and turbulent layer called the magnetosheath. Magnetosheath jets are localised pulses of high-dynamic pressure plasma originating at the terrestrial bow shock and propagating Earthward through the magnetosheath. As flows of mass and energy they couple the solar wind and foreshock to the magnetopause and magnetosphere. In this thesis we investigate several aspects of magnetosheath jets using a database of over 13,000 jets observed by the THEMIS spacecraft over 11 years. Using simultaneous measurements of the upstream solar wind, we explore how the solar wind controls jet formation and propagation, finding that jets reach the magnetopause 17x more often during low IMF cone angle solar wind, and 8x more during high solar wind speeds, compared to the opposite condition. We investigate the properties of jets in the magnetosheath, comparing observations near the bow shock and near the magnetopause. We find that jets typically possess higher β than their surroundings at the magnetopause, making jet plasma likely to suppress reconnection according to the Δβ-shear condition. Despite this, we see that individual jets exhibit sufficient magnetic field fluctuation such that most jets may be able to alter reconnection from what would be expected from the IMF, that is, trigger it during northward IMF and suppress it during southward IMF. Using a rich and complex case study example, we explore the magnetopause response to jet impacts, finding jets to be intrinsically linked to localised bursty reconnection and magnetopause dynamics, while developing analysis tools for application to similar events. The results shown in this thesis represent a significant advancement towards being able to forecast the space weather effects arising from magnetosheath jets.