Heat and composition transport in gas giant planets and exoplanets The growing collection of directly-imaged young gas giant planets together with the new results from the Juno spacecraft on Jupiter's interior provide new ways to constrain the physics of gas giant formation and evolution. In this talk, I will focus on two outstanding questions: how accretion sets the luminosity of newly-formed gas giants, and how the composition profile interacts with convection during the planet's evolution. Resolving these open questions is crucial if we are to connect planet formation models to Jupiter today.