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In this article, we present the recent advances in the development of the anisotropic phase-field crystal (APFC) model. These advances are important in basic researches for multiferroic and thermoelectric materials with anisotropic crystal lattices and in thin-film applications. We start by providing a general description of the model derived in our previous studies based on the crystal symmetry and the microscopic dynamical density functional theory for anisotropic interactions and show that there exist only two possible degrees of freedom for the anisotropic lattices which are described by two independent parameters. New findings concerning the applications of the APFC model for the estimation of the elastic modules of anisotropic systems including sheared and stretched lattices as well as for the investigation of the heterogeneous thin film growth are described. The simulation results demonstrate the strong dependency of the misfit dislocation formation during the film growth on the anisotropy and reveal the asymmetric behavior in the cases of positive and negative misfits. We also present the development of the amplitude representation for the full APFC model of two orientation variants and show the relationship between the wave vectors and the base angles of the anisotropic lattices.