The dynamics of wave propagation and wave transport are reviewed for vertically propagating, forced, planetary scale waves in the middle atmosphere. Such waves can be divided into two major classes: extratropical planetary waves and equatorial waves. The most important waves of the former class are quasi-stationary Rossby modes of zonal wavenumbers 1 and 2 (1 or 2 waves around a latitude circle), which propagate vertically only during the winter season when the mean winds are westerly. These modes transport heat and ozone towards the poles, thus maintaining the mean temperature above its radiative equilibrium value in high latitudes and producing the high latitude ozone maximum. It is shown that these wave transport processes depend on wave transience and wave damping. The precise form of this dependency is illustrated for transport of a strongly stratified tracer by small amplitude planetary waves. The observed equatorial wave modes are of two types: an eastward propagating Kelvin mode and a westward propagating mixed Rossby-gravity mode. These modes are thermally damped in the stratosphere where they interact with the mean flow to produce eastward and westward accelerations, respectively. It is shown that in the absence of mechanical dissipation this wave-mean flow interaction is caused by the vertical divergence of a wave `radiation stress'. This wave-mean flow interaction process is responsible for producing the well known equatorial quasi-biennial oscillation.