Abstract: Large scale internal waves are frequently present in certain parts of our oceans.   The lecture will begin with a precis of this phenomenon, followed by some recently derived models for internal wave propagation.  The discussion will then turn to mathematical analysis concerning these coupled systems of partial differential equations which feature non-local operators.  The discussion will conclude with a set of numerical simulations illustrating some of the spatial dynamics of solutions and applications of the model to some interesting oceanographic phenomena.