  The generic nature of band touching points in three-dimensional band
structures is at heart of the rich phenomenology, topological stability and
novel Fermi arc surface states associated with Weyl semimetals. Here we report
on the corresponding scenario emerging in systems effectively described by
non-Hermitian Hamiltonians. Remarkably, three-dimensional non-Hermitian systems
have generic band touchings along one-dimensional closed contours forming
exceptional rings and links in reciprocal space. The associated Seifert
surfaces support open "Fermi ribbons" where the real part of the energy gap
vanishes, providing a novel class of higher-dimensional bulk generalisations of
Fermi arcs which are characterised by an integer twist number. These results
have possible applications to a plethora of physical settings ranging from
mechanical systems and optical metamaterials with loss and gain to heavy
fermion materials with finite-lifetime quasiparticles. In particular, photonic
crystals provide fertile ground for simulating the exuberant phenomenology of
exceptional links and their concomitant Fermi ribbons.
