The atmospheric circulation on Jupiter, Saturn, Uranus and Neptune is dominated by strong east-west jet-streams. In this talk we will discuss the physical mechanisms controlling these jets, focusing on the depth to which they extend into the planets' fluid interiors. New information about the vertical structure of these winds is expected in 2016 when NASA's Juno and Cassini spacecraft will perform close flybys of Jupiter and Saturn, obtaining for the first time a high order gravity spectrum of these planets. We will show how the relations between the fluid velocity and the measured gravity perturbations due to dynamics can be used to constrain the depth of the circulation on these planets. We find that for the case of Uranus and Neptune, even the already known values of the fourth zonal gravity harmonic, J4, can constrain the observed zonal jets to a thin weather-layer containing no more than the uppermost 0.2% of the planetary mass.