Two-dimensional electron gas (2DEG) in microwave irradiation has been an intriguing system to study transport properties of electrons for a decade, during which extensive important phenomena have been discovered, such as microwave induced resistance oscillation (MIRO), zero resistance state(ZRS) and zero conductance state(ZCS). Along this direction, this thesis is devoted to new phenomena recently discovered in such systems, 1) microwave induced cyclotron harmonic peak (2wc spike) in ultraclean 2DEG without antidots inducing electric modulation potential 2) Aharonov- Bohm(AB) oscillations in microwave irradiated 2DEG with modulation potential. Those phenomena originate from quantum interference, from either interplay between two different kinds of scattering or different electrons transition paths. In addition to microwave induced phenomena, other nonlinear effects such as Zener tunneling and geometric resonance(GR) have been investigated further in the past few years and collected in this thesis. Zener tunneling has been found in two-dimensional hole gas(2DHG) with a large damping factor, which inspires more questions on the unique band structures of holes. GR has been studied in ultra-clean modulated 2DEG , in which more oscillation peaks show up. In the GR regime with an inplane magnetic field applied, the antisymmetric hall oscillations lead us to propose the existence of a magnetic lattice along with an artificial antidots lattice and a current lattice in such systems.