  The quantum Hall (QH) effect represents a unique playground where quantum
coherence of electrons can be exploited for various applications, from
metrology to quantum computation. In the fractional regime it also hosts
anyons, emergent quasiparticles that are neither bosons nor fermions and
possess fractional statistics. Their detection and manipulation represent key
milestones in view of topologically protected quantum computation schemes.
Exploiting the high degree of phase coherence, edge states in the QH regime
have been investigated by designing and constructing electronic
interferometers, able to reveal the coherence and statistical properties of the
interfering constituents. Here, we review the two main geometries developed in
the QH regime, the Mach-Zehnder and the Fabry-Perot interferometers. We present
their basic working principles, fabrication methods, and the main results
obtained both in the integer and fractional QH regime. We will also show how
recent technological advances led to the direct experimental demonstration of
fractional statistics for Laughlin quasiparticles in a Fabry-Perot
interferometric setup.
