Abstract: Heavy-ion collisions provide a unique opportunity to study the nuclear equation of state for a wide range of densities, temperatures, and neutron-proton asymmetries in the laboratory. Transport models are the main method to obtain physics information on the nuclear equation of state and in-medium properties of particles from low to relativistic-energy heavy-ion collisions. In this paper, the typical transport models used in heavy ion collisions were introduced, including the phenomenology-type transport model, such as dinuclear system (DNS) model and Langevin equation, Boltzmann-equation and quantum molecular dynamics (QMD) type transport model. Besides, some of their computed results were taken as examples to introduce the progress of transport theory. The difficulties faced by the current transport model were also summarized, and the application of machine learning in heavy ion collisions transport theory was reviewed. In this area, machine learning, especially deep learning, has been widely used as a significant data analysis method. Machine learning could be applied to correct the input of transport model, such as the nuclear equation of state and impact parameter, and constrain the output results, such as fission yields. The convolutional neural networks (CNN), light gradient boosting machine (LightGBM), Bayesian neural network (BNN) were introduced in these studies mentioned. Based on the above, the key problems to be solved possibly using machine learning in transport theory were proposed: Nucleon-nucleon correlations are not included in Boltzmann-type transport model, due to the basic assumptions needed to derive Boltzmann equation from Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equations, which are Rarefied gas hypothesis and Stosszahlansatz; Only two-body collision is considered in Boltzmann equation without N-body collisions, which is unphysical in high density. High order terms of BBGKY equations need to be considered; The fermionic nature of the system should be preserved in the evolution of nuclear reaction system, but is lost rapidly in QMD-type transport model because of fluctuations, even with Fermi statistics implemented at the beginning of the reaction and the Pauli principle enforced in the collision term; The multi-time scale should be used to deal with the evolution from the collision stage to the local equilibrium, which has to be ignored in the current transport theory; Incomplete experimental data are available as input of transport model, which leads to improve the accuracy of the transport model. The solution of above problems is expected to combine machine learning and transport theory. These studies are essential for further developments of precise transport model.