We investigate integer and fractional quantum Hall states in quantum point contacts (QPCs) of different geometries, defined in AlGaAs/GaAs heterostructures employing different doping and screening techniques. We find that, even in the highest mobility samples, interference and localization strongly influence the transport properties. We propose microscopic models for these effects, based on single- and many-electron physics. For integer quantum Hall states, transport is modulated due to the

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... -consistent formation of compressible regions of enhanced or reduced density in the incompressible region of the constriction. In the fractional quantum Hall regime, we observe the localization of fractionally charged quasi-particles in the constriction and an interplay of single- and many-electron physics. At low electron densities and in comparatively weak magnetic fields, single-electron interference dominates transport. Utilizing optimized growth and gating techniques, the ν=5/2 state can be observed in a QPC, conserving the bulk properties in an unprecedented quality. Our results might improve the understanding of the influence of localization on the transmission properties of QPCs, which is necessary for the interpretation of interference experiments employing QPCs, especially at ν=5/2.