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Fano models - consisting of a Hamiltonian with discrete-continuous spectrum -are one of the basic toy models in spectroscopy. They have been succesfull inexplaining the lineshape of experiments in atomic physics and condensed matter.These models however have largely been out of the scope of dissipativedynamics, with ony a handful of works considering the effect of a thermal bath.Yet in nanostructures and condensed matter systems, dissipation stronglymodulates the dynamics. In this article, we present an overview of thetheoretical works dealing with Fano interferences coupled to a thermal bath andcompare them to the scattering formalism. We provide the solution to anydiscrete-continuous Hamiltonian structure within the wideband approximationcoupled to a Markovian bath. In doing so, we update the toy models that havebeen available for unitary evolution since the 1960s. We find that the Fanolineshape is preserved as long as we allow a rescaling of the parameters, andan additional Lorentzian contribution that reflects the destruction of theinterference by dephasings. We discuss the pertinence of each approach -dissipative and unitary - to different experimental setups: scattering,transport and spectroscopy of dissipative systems. We finish by discussing thecurrent limitations of the theories due to the wideband approximation and thememory effects of the bath.

On the ubiquity of Beutler-Fano profiles: from scattering to dissipative processes