The polarization and domain structure of ferroelectric compounds and especially the switching thereof are difficult to access by experimental means. This is due to the microscopic nature and the fast dynamics of the underlying physical phenomena. Therefore, we use simulations on the atomic (classical molecular dynamics or MD) and electronic (density functional theory, DFT) scale. They deliver accurate and detailed insights necessary to understand a material at the microscopic scale. In MD atoms are modeled as point masses that interact via effective potentials. Becoming increasingly complex these potentials allow description of many physical effects in ferroelectrics. For an efficient performance of the simulation we use the open-source computer code LAMMPS which works excellently on highly parallel computing clusters. In contrast, DFT also assumes atoms to be classical point masses but, additionally, includes a quantum mechanical treatment of the electron density. These simulations have the advantage of strongly increased accuracy at the cost of heavily increased computational load. Again an open-source solution, the computer code Abinit, implements an efficient framework for performing such calculations.