The Juno mission to the planet Jupiter has revealed significant new information about the processes going on inside the planet. Similar data for Saturn was obtained from the Cassini grand finale. Accurate measurements of Jupiter's gravity fields has shown that the odd spherical harmonic components of the gravity field are non-zero, and a natural explanation of this is that the fast winds at the surface extend thousands of kilometres below the surface, possibly down to the electrically conducting region where magnetic fields become significant. Saturn's zonal flows extend even deeper than those on Jupiter, so that both the even and odd spherical harmonic coefficients are significantly affected by the flow. The way in which information about the deep flows can be deduced from the gravity coefficients will be discussed. The missions also revealed new data about the magnetic fields of the giant planets, which can be compared with the magnetic fields found from dynamo models. These fields arise because at high pressure hydrogen becomes metallic, and hence electrically conducting. Saturn's magnetic field is remarkably axisymmetric, and Jupiter's magnetic field has a much greater asymmetry between the northern and southern hemispheres than is found in the Earth's magnetic field. Possible reasons for this will be discussed. The ongoing Juno mission raises the prospect of detecting changes in Jupiter's magnetic field with time, which could indicate how deep flows interact with magnetic fields.