Abstract: Spin-related physics are hot topics in various research fields. Nucleons and quarks are both spin-half fermions. They are affected by the spin-orbit interaction as well as the magnetic field in non-central heavy-ion collisions, leading to interesting spin dynamics, especially the spin polarization perpendicular to the reaction plane. In relativistic heavy-ion collisions, the produced quarks can be approximately considered as massless particles due to the extremely high temperatures and high densities reached there, and the spin dynamics turns to the chiral dynamics in this case. Under the external electromagnetic field and vortical field, a series chiral anomaly effects may appear once there are asymmetries of electric charges and/or chirality charges. This manuscript reviews a series of studies on the spin and chiral dynamics based on transport simulations from our research group, including particle spin polarizations in intermediate-energy heavy-ion collisions and relativistic heavy-ion collisions, as well as chiral magnetic waves in an ideal system and in relativistic heavy-ion collisions.