The chiral rotation in atomic nuclei has attracted significant attention in recent years. This paper introduces the particle rotor model and the titled axis cranking model, which are used to analyze the chiral rotation with multi-quasiparticle configuration. {For the particle rotor model, the basis space and the method to solve the model are discussed in detail: by considering the single-particle states of valence nucleons and the selection rule of angular momentum, one can construct the strong coupling basis which is symmetrized under the point group $D_2$; the dimension of the basis space will be very large when several valence nucleons are included, thus the Lancozos method is adopted to diagonalize the large scale hamiltonian matrix. For the titled axis cranking model, two versions based on the pairing plus quadrupole model and the shell correction method are introduced respectively: the cranking Hartree-Fock-Bogoliubov equations are given starting with the two-body Routhian; the 3-dimensional tilted axis cranking solutions are discussed in the intrinsic principal axes frame, and the vector of the angular velocity is parallel with the vector of the expectation values of the angular momentum components when the self-consistent solution is obtained.} By summarizing and developing further the two models, it will be helpful to clarify the debates in the understanding of the nuclear chiral rotation.