In this report, we review the isospin dependence of various forms of the collective flow in heavy-ion reactions from Fermi to relativistic energies. The emphasis will be on suggested possible applications in directly exploring the underlying isovector potential and thus the Equation of State (EoS) of asymmetric nuclear matter, in particular in density regions far away from normal conditions. We also discuss forthcoming challenges and opportunities provided by high-energy radioactive beams. Societ Italiana di Fisica and Springer-Verlag 2006.
