Internal gravity waves exist in density stratified fluids where they are driven by gravitaitonal restoring forces. They play a crucial role in the transfer of energy from large scales where it is injected to small scales where it is injected. Internal waves observed in the ocean are often subject to significant nonlinear effects which arise in a variety of ways. In this talk I will focus on nonlinear horizontally propagating internal waves. Weakly-nonlinear waves can be described by the Gardner equation (KdV plus cubic nonlinearity) or, in the context of wave packets, by the NLS equation. Both of these equations have two different forms. The Gardner+ equation has solitary waves of two polarities (i.e. waves of depression and of elevation) with one branch having a minimum amplitude. It also has breather solutions. The Gardner- equation has only a single branch of solitary wave solutions with a limiting amplitude and no breather solutions. The behaviour of the solutions of the Gardner equation will be compared with solutions of the fully nonlinear-dispersive solutions of the Dubreil-Jacotin-Long (DJL) equation. The NLS equation also has two forms: NLS+ and NLS-. Example stratifications will be presented showing that both NLS+/- may arise in applications depending on the wave-length and stratification. The behaviour of the solutions of the Gardner equation will be compared with solutions of the fully nonlinear-dispersive solutions of the Dubreil-Jacotin-Long (DJL) equation and results from nonlinear simulations of the incompressible Euler equations (with the Boussinesq approximation) will shown to illustrate solitary waves and breathers in the full nonlinear governing equations.