This article summarizes theoretical predictions for the density and isospin
dependence of the nuclear mean field and the corresponding nuclear equation of
state. We compare predictions from microscopic and phenomenological approaches.
An application to heavy ion reactions requires to incorporate these forces into
the framework of dynamical transport models. Constraints on the nuclear
equation of state derived from finite nuclei and from heavy ion reactions are
discussed.Comment: 17 pages, 13 figures, contributed paper to the World Consensus
Initiative (WCI) book "Dynamics and Thermodynamics with Nucleonic Degrees of
Freedom