The Galileo and Cassini spacecrafts have greatly enhanced the observational record of Jupiter's tropospheric dynamics, particularly through returning high spatial resolution, multi-spectral and global imaging data with episodic coverage over periods of months to years. These data, along with those from Earth-based telescopes, have revealed the stability of Jupiter's zonal jets, captured the evolution of vortices and equatorial waves, and mapped the distributions of lightning and moist convection. Because no observations of Jupiter's interior exist, a forward modelling approach has been used to relate observations at cloud level to models of shallow or deep jet structure, shallow or deep jet forcing and energy transfer between turbulence, vortices and jets. A range of observed phenomena can be reproduced in shallow models, though the Galileo probe winds and jet stability arguments hint at the presence of deep jets. Many deep models, however, fail to reproduce Jupiter-like non-zonal features (e.g. vortices). Jupiter's dynamics likely include both deep and shallow processes, requiring an integrated approach to future modelling—an important goal for the post-Galileo and Cassini era.