This dissertation describes quantum Hall transport experiments on Fabry-Perot electron interferometers fabricated from GaAs/AlGaAs heterostructure material. The devices consist of an island separated from the two-dimensional (2D) electron bulk via two tunable constrictions. Front gates deposited in etch trenches permit to fine tune the device. When tunneling occurs in the constrictions, electrons perform closed orbits around the island, producing an Aharonov-Bohm oscillatory signal in the conductance. Quantized plateaus in longitudinal and Hall resistances of the device allow us to determine the Landau level filling in both the bulk and the constriction.A comprehensive experimental characterization of quantum Hall and Shubnikovde Haas (SdH) transport is presented in the first interferometer. Application of front-gate voltage affects the constriction electron density, but the 2D bulk density remains unaffected. Analyzing the data within a Fock-Darwin model, we obtain the front-gate bias dependencies of constriction electron density, and, extrapolating to zero magnetic field, the number of 1D electric subbands resulting from the electron confinement in the constrictions.In the same interferometer, by carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition.In the second interferometer, etch trench depletion is such that in the fractional quantum Hall (FQH) regime, filling 1/3 current-carrying chiral edge channels pass through the constrictions and encircle an island of the 2/5 FQH fluid. In this regime, we observe magnetic flux and charge periods 5h/e and 2e, respectively, corresponding to creation of ten e/5 Laughlin quasiparticles in the island. The observed experimental periods are interpreted as imposed by the anyonic statistical interaction of fractionally charged quasiparticles.