  Nowadays nanotechnology allows to scale-down various important devices
(sensors, chips, fibres, etc), and, thus, opens up new horizon for their
applications. Nevertheless, the efficiency most of them is still based on the
fundamental physical phenomena, such as resonances. Thus, the understanding of
the resonance phenomena will be beneficial. One of the well-known examples is
the resonant enhancement of the transmission known as Breit-Wigner resonances,
which can be described by a Lorentzian function. But, in many physical systems
the scattering of waves involves propagation along different paths, and, as a
consequence, results in interference phenomena, where constructive interference
corresponds to resonant enhancement and destructive interference to resonant
suppression of the transmission. Recently, a variety of experimental and
theoretical work has revealed such patterns in different branches of physics.
The purpose of this Review is to demonstrate that this kind of resonant
scattering is related to the Fano resonances, known from atomic physics. One of
the main features of the Fano resonances is the asymmetric profile. The
asymmetry comes from the close coexistence of resonant transmission and
resonant reflection. Fano successfully explained such a phenomenon in his
seminal paper in 1961 in terms of interaction of a discrete (localized) state
with a continuum of propagation modes. It allows to describe both resonant
enhancement and resonant suppression in a unified manner. All of these
properties can be demonstrated in the frame of a very simple model, which will
be used throughout the Review to show that resonant reflections observed in
different complex systems are indeed closely related to the Fano resonances.
