With experimental facilities being developed globally, producing superheavy nuclei using heavy-ion collision has become feasible, which is essential for exploring charge and mass limits of nuclei and understanding the r-process in nuclear astrophysics. Fusion reactions are crucial for the synthesis of superheavy nuclei, yet only neutron-deficient superheavy nuclei get produced due to the limited neutron number of stable beams. Recent experiments suggest that multinucleon transfer reactions are promising for producing new neutron-rich superheavy nuclei. As a result, transport models are required for extracting physics information from these experiments and making predictions about incident energies and projectile-target combinations, to synthesize new super-heavy nuclei. In this article, we introduce the development of transport models such as the dinuclear system (DNS) model, quantum molecular dynamics (QMD) type model, Boltzmann type model, and Time-dependent Hatree-Fock (TDHF) type model, and conclude with their latest applications in the synthesis of superheavy nuclei, especially in fusion reactions and multinucleon transfer reactions. In addition, various international large-scale scientific facilities, as well as their scientific objectives, and future plans, are also summarized.