Magnetic particle imaging (MPI) estimates the spatial distribution of super-paramagnetic iron-oxide nanoparticles (SPIOs) via the magnetization response of the particles subjected to static and ocillatory magnetic fields. This book focuses on the physics of the SPIOs with emphasis to the application in MPI and gives a brief introduction to the related particle physics. Stochastical Langevin equations are used to simulate the magnetization response. The stochastic differential equations, which incorporate the Néel and the Brown relaxation processes, are derived in detail and solved numerically. The solutions are validated with respect to the related Fokker-Planck equation. Subsequently, simulation studies are carried out to compare different particle parameters like the hydrodynamic diameter or the particle anisotropy with respect to the frequency of the magnetic excitation fields. In addition, a less complex particle model based on ordinary differential equations is presented to fit measurement data of a magnetic particle spectrometer. This optimization task is carried out by a new 2-dimensional continuous genetic algorithm.