<p>Toroidal rotation in Tokamak plasmas can suppress magnetohydrodynamic (MHD) instabilities, which can improve the plasma confinement. Experiments show that the rotation can be generated without momentum input, which is the so-called intrinsic rotation due to turbulent transport. This review summarizes the microscopic theory of ion parallel momentum turbulent transport, including kinetic theory with electrostatic and electromagnetic turbulence in slab geometry, toroidal effects and strong turbulent transport. It is shown that only resonant particles contribute to the ion parallel momentum transport and non-resonant terms correspond to the parallel momentum of waves. Microscopic pictures are provided for both electrostatic and electromagnetic cases to demonstrate the exchange of parallel momentum between ions and waves. The resonant momentum flux can be taken as a convection induced by resonant ions. And the resonant source term is the exchanging rate of parallel momentum between resonant ions and waves. In the electromagnetic model, through the transformation of the fluctuating magnetic field, the poloidal flow and perturbed magnetic field under Lorentz transformation furnish turbulence intensity and generate a parallel electric field that accelerates particles. Moreover, it is revealed that the finite orbit width effects due to the toroidal geometry can induce a Coriolis drive term, which spontaneously breaks the toroidal symmetry. Finally, it is found that, in strong turbulence case, the contour of coherent structures can affect the nonlinear momentum flux and potentially convect the parallel momentum inward.</p>