Magnetic particle imaging (MPI) is a recent imaging modality that uses nonlinear magnetization curves of the superparamagnetic iron oxides. One of the main assumptions in MPI is that the selection field changes linearly with respect to the position, whereas in practice it deviates from its ideal linearity in regions away from the center of the scanner. The first part of this thesis demonstrates that unaccounted non-linearity of the selection field causes warping in the image reconstructed with a standard x-space approach. Unwarping algorithms can be applied to effectively address this issue, once the displacement map acting on the reconstructed image is determined. The unwarped image accurately represents the locations of nanoparticles, albeit with a resolution loss in regions away from the center of the scanner due to the degradation in selection field gradients. In MPI, the relaxation behavior of the nanoparticles can also be used to infer about nanoparticle characteristics or the local environment properties, such as viscosity and temperature. As the nanoparticle signal also changes with drive field (DF) parameters, one potential problem for quantitative mapping applications is the optimization of these parameters. In the second part of this thesis, a novel accelerated framework is proposed for characterizing the unique response of a nanoparticle under different environmental settings. The proposed technique, called “Magnetic Particle Fingerprinting” (MPF), rapidly sweeps a wide range of DF parameters, mapping the unique relaxation fingerprint of a sample. This technique can enable simultaneous mapping of several parameters (e.g., viscosity, temperature, nanoparticle type, etc.) with significantly reduced scan time.