In the past five years there have been significant advances in dynamical 
systems theory to the point where the framework can now be utilized in the 
context of "real" problems. In this talk we will briefly describe the dynamical 
systems framework for Lagrangian transport. In particular, we will show how data 
sets, such as those derived from remote sensing observations (such as high 
frequency radar arrays) or the output of a large scale numerical computation, 
can be viewed as dynamical systems. We will illustrate these ideas by 
introducing several examples; transport in a coastal system using a velocity 
field obtained experimentally from high frequency radar measurements and 
transport in a wind driven double gyre system. The point of view of a dynamical 
system as a data set gives rise to new mathematical problems in the theory of 
dynamical systems. These will be briefly mentioned, but the focus will be on 
showing how dynamical systems theory applies and gives new insight and results 
on transport and predictability of transport processes. Finally, we will discuss 
other problems where the dynamical systems approach to transport may have a 
major impact in the future.