Internal gravity waves are a common feature of stratified fluids. They facilitate transport of momentum and energy – thus influencing the evolution of the fluid. There is a large body of research addressing the behaviour of gravity waves in the terrestrial atmosphere. This thesis builds and extends the research to giant planets – in particular to close-in extrasolar giant planets and the solar system giant planet, Jupiter. Because the atmospheres of close-in giant planets are expected to be strongly stratified, knowledge of the behaviour of gravity waves in such atmospheres is especially important. Close-in giant planets are thought to have their rotations and orbital period 1:1 synchronised, i.e., they are “tidally locked”. Such planets do not exist in the Solar System. However, many are known from observations of extrasolar systems. Their synchronisation means that they have a permanent day-side and night-side leading to interesting atmospheric dynamics. Modelling these circulations with global circulation models (GCMs) and comparing these models with observations is an active research area. However, many GCMs filter some or all gravity waves removing their effects. This thesis addresses this by explicitly looking at the effects gravity waves can have on the circulation. It is shown that gravity waves provide a mechanism for accelerating, decelerating, and heating the flow. Further, horizontally propagating gravity waves are shown to provide a possible means for coupling the day- and night-sides of tidally locked planets. As well as affecting the dynamics of the atmosphere, gravity wave behaviour is affected by the dynamics of the atmosphere. Therefore, gravity waves can be used to explore atmospheric properties. In this thesis gravity waves observed in Jupiter’s atmosphere, by the Galileo probe, are used to identify features of Jupiter’s atmosphere such as the altitude of the turbopause and the vertical profile of zonal winds at the probe entry site.