Eulerian transport measures net amount of fluid particles and properties such 
as temperature and salinity, which migrate from one region to another across a 
stationary boundary over a time interval. In this talk we present a new 
theoretical framework for Eulerian transport where the stationary boundary is 
defined by a reference streamline based on dynamical systems approach. Our 
theory provides us with quantitative as well as geometrical information 
concerning Eulerian transport across any reference streamline over a finite or 
infinite time interval. Its relation to Lagrangian transport theory can be 
rigorously shown when the stationary boundary is chosen to compute the terminal 
transport between kinematically distinct flow regions. We demonstrate our theory 
using a data set obtained by numerical simulation of mid-latitude wind-driven 
ocean circulation. Finally we discuss future applications of Eulerian transport 
in physical oceanography.