This dissertation describes low-temperature electronic transport measurements on semiconductor structures of restricted dimensionality. The experiments fall into two sets. The first concerns anisotropic magnetotransport measurements and electron focusing in a varying external magnetic field. These are performed using MBE-grown high mobility two-dimensional electron gases formed on (311)B GaAs substrates. The second is a study of magnetic field induced insulator-quantum Hall liquid transitions performed on GaAs-AIGaAs heterostructures in which a number of InAs monolayers are inserted in the centre of a GaAs quantum well. The sample structures were characterised by STM, TEM, STEM, and AFM. Interest in electron transport on high-index GaAs surfaces is increasing, especially since the advent of patterned substrate regrowth. An anisotropic mobility in orthogonal directions seems to be universal for electron gases grown on (311)B-oriented GaAs substrates. The anisotropy depends on the two-dimensional electron gas carrier density, but mobilities are always higher in the [233] direction. The interface roughness scattering is a possible cause of the mobility anisotropy. The electron focusing results demonstrate that the effective mass and Fermi surface are isotropic even through the mobility is anisotropic. An explanation is proposed based on interface roughness scattering. In the second part, a magnetically induced direct transition from an insulating state at zero magnetic field to quantum Hall effect states with Hall resistance Pxy = h/2e2 and Pxy = h/e2 and back to an insulating state at higher field is observed. The phase boundaries are plotted as a function of disorder and magnetic field using two methods, firstly the temperature independent Pxx points and secondly the maxima in CJxx. This experimental phase diagram is related to the disorder induced collapse of spin splitting in the lowest Landau level obtained from activation energy studies.