Numerical and theoretical studies of internal gravity waves have been performed to understand the role of convective instabilities in nonlinear, large amplitude gravity waves; the effects of saturation and self acceleration on transient gravity wave, mean flow interaction; the role of local convective instabilities in producing turbulent modifications of potential temperature and trace constituents in breaking gravity waves; and the propagation and refraction of inertial and non inertial gravity waves through observed middle atmosphere wind fields. Simulations with a two dimensional, nonhydrostatic gravity wave model indicate that convective adjustment in unstable gravity waves results in a mean flow modification closely approximated by WKB saturation theory in cases where the incident wave field is nearly monochromatic. Convection also limits, and practically prevents, the evolution to a reflecting nonlinear critical layer, even when the incident wave field is not monochromatic. Some critical layer dislocation is observed due to self acceleration in transient gravity waves. Localization of turbulence in a convectively unstable gravity wave can greatly reduce the mixing of heat and trace constituents and implies a large turbulent Prandtl number. Significant lateral movement and refraction of gravity wave rays is observed for inertia gravity waves in realistic wintertime flows. A formula is derived for the onset of dynamical instability in inertia-gravity waves, having a lower threshold than the corresponding amplitude required for convective instability.