The optimization of magnetic nanoparticles (MNPs) as markers for magnetic particle imaging (MPI) requires an understanding of the relationship between the harmonics spectrum and the structural and magnetic properties of the MNPs. Although magnetic particle spectroscopy (MPS) - carried out at the same excitation frequency as the given MPI system - represents a straightforward technique to study MNPs for their suitability for MPI, a complete understanding of the mechanisms and differences between different tracer materials requires additional measurements of the static and dynamic magnetic behavior covering additional field and time ranges. Furthermore, theoretical models are needed, which correctly account for the static and dynamic magnetic properties of the markers. In this paper, we give an overview of currently used theoretical models for the explanation of amplitude and phase of the harmonics spectra as well as of the various static and dynamic magnetic techniques, which are applied for the comprehensive characterization of MNPs for MPI. We demonstrate on two multicore MNP model systems, Resovist(®) and FeraSpin™ Series, how a detailed picture of the MPI performance can be obtained by combining various static and dynamic magnetic measurements.