Two-dimensional electron (2DES) and hole (2DHS) systems have attracted intense research attentions in past decades. A 2DES or 2DHS modulated by one-dimensional or two-dimensional spatially periodic potential shows particular importance because the existence of modulation provides a tunable parameter for exploring interaction between electrons and scattering centers presenting on the two-dimensional systems. This thesis documents a systematic experimental study, in collaboration with Bell Labs, of electronic transport in very-high mobility 2DES and 2DHS in GaAs/AlGaAs quantum structures. Fabrication of triangular antidot lattice in 2DES, as well as low-temperature transport and photoconductivity properties in spatially modulated 2DES, has been studied. Strong Geometric resonance (GR), up to seven peaks resolved, is observed in the longitudinal magnetoresistance because of high mobility of 2DES after fabrication of antidot lattice. Photoresistance shows clear millimeterwave-induced resistance oscillations (MIRO) but with heavily damping amplitudes, and magnetoplasmon resonance (MPR) is also observed as well. GR, MIRO and MPR are decoupled from each other in our modulated 2DES. These experimental findings pave the way for studies of nonlinear transport in modulated 2DES. Magnetotransport measurements on a new material, the Carbon δ-doped 2DHG in GaAs/AlGaAs quantum well, indicate that the 2DHG has a transport scattering time compatible with those in very-high mobility 2DES. However, photoresistance measurement shows much weaker MIRO in the 2DHS than that in 2DES with compatible transport scattering time. Low-temperature transport measurements on Landau, Zeeman, and spin-orbital parameters imply that the C-doped 2DHS has small zero field spin splitting and large effective g-factor. As part of the thesis work, the thesis also presents a development of low-temperature/high magnetic field (300mK/12T) scanning Hall probe microscope (SHPM) technique for measuring small local magnetic fields at low temperature and an algorithm for calculating the current density from measured magnetic fields based on Fourier transformation technique. Integration of SHPM and the algorithm provides a practical tool for imaging the current distribution and a powerful method to explore electronic transport properties of 2DES and 2DHS.