The equation of state (EOS) of nuclear matter,i.e.,the thermodynamic relationship between the binding energy per nucleon,temperature,density,as well as the isospin asymmetry,has been a hot topic in nuclear physics and astrophysics for a long time.The knowledge of the nuclear EOS is essential for studying the properties of nuclei,the structure of neutron stars,the dynamics of heavy ion collision (HIC),as well as neutron star mergers.HIC offers a unique way to create nuclear matter with high density and isospin asymmetry in terrestrial laboratory,but the formed dense nuclear matter exists only for a very short period,one cannot measure the nuclear EOS directly in experiments.Practically,transport models which often incorporate phenomenological potentials as an input are utilized to deduce the EOS from the comparison with the observables measured in laboratory.The ultrarelativistic quantum molecular dynamics (UrQMD) model has been widely employed for investigating HIC from the Fermi energy (40 MeV per nucleon) up to the CERN Large Hadron Collider energies (TeV).With further improvement in the nuclear mean-field potential term,the collision term,and the cluster recognition term of the UrQMD model,the newly measured collective flow and nuclear stopping data of light charged particles by the FOPI Collaboration can be reproduced.In this article we highlight our recent results on the studies of the nuclear EOS and the nuclear symmetry energy with the UrQMD model.New opportunities and challenges in the extraction of the nuclear EOS from transport models and HIC experiments are discussed.