We study relative dispersion of passive scalar in non-ideal cases, i.e. in 
situations in which asymptotic techniques cannot be applied; typically when the 
characteristic length scale of the Eulerian velocity field is not much smaller 
than the domain size. Of course, in such a situation usual asymptotic quantities 
(the diffusion coefficients) do not give any relevant information about the 
transport mechanisms. On the other hand, we shall show that the Finite Size 
Lyapunov Exponent, originally introduced for the predictability problem, appears 
to be rather powerful in approaching the non-asymptotic transport properties. 
This technique is applied in a series of numerical experiments in simple flows 
with chaotic behaviors, in experimental data analysis of drifter and to study 
relative dispersion in fully developed turbulence.