Constraints on the Equation of State for symmetric matter (equal neutron and proton numbers) have been extracted from energetic collisions of heavy ions over a range of energies.Collisions of neutron-deficient and neutron-rich heavy ions now provide initial constraints on the EoS of neutron-rich matter at sub-saturation densities from isospin diffusions and neutron proton ratios.These constraints are compared to other available constraints from nuclear structures and masses and to constraints obtained at supra-normal densities.This work is supported by the National Science Foundation under Grant Nos.PHY-0606007.