This thesis consists of two parts. The first part considers the effect of microwave radiation on magnetotransport in high quality GaAs/AlGaAs heterostructure two dimensional electron systems. The effect of microwave (MW) radiation on electron temperature was studied by investigating the amplitude of the Shubnikov de Haas (SdH) oscillations in a regime where the cyclotron frequency $\omega_{c}$ and the MW angular frequency $\omega$ satisfy $2\omega \leq \omega_{c} \leq 3.5\omega$. The results indicate negligible electron heating under modest MW photoexcitation, in agreement with theoretical predictions. Next, the effect of the polarization direction of the linearly polarized MWs on the MW induced magnetoresistance oscillation amplitude was investigated. The results demonstrate the first indications of polarization dependence of MW induced magnetoresistance oscillations. In the second part, experiments on the magnetotransport of three dimensional highly oriented pyrolytic graphite (HOPG) reveal a non-zero Berry phase for HOPG. Furthermore, a novel phase relation between oscillatory magneto- and Hall- resistances was discovered from the studies of the HOPG specimen.

Previous studies have demonstrated the sensitivity of the amplitude of the microwave radiation-induced magnetoresistance oscillations to the microwave polarization. These studies have also shown that there exists a phase shift in the linear polarization angle dependence. But the physical origin of this phase shift is still unclear. Therefore, the first part of this dissertation analyzes the phase shift by averaging over other small contributions, when those contributions are smaller than experimental uncertainties. The analysis indicates nontrivial frequency dependence of the phase shift. The second part of the dissertation continues the study of the phase shift and the results suggest that the specimen exhibits only one preferred radiation orientation for different Hall-bar sections. The third part of the dissertation summarizes our study of the Hall and longitudinal resistance oscillations induced by microwave frequency and dc bias at low filling factors. Here, the phase of these resistance oscillations depends on the contact pair on the device, and the period of oscillations appears to be inversely proportional to radiation frequency.