  The search of topological states in non-Hermitian systems has gained a strong
momentum over the last two years climbing to the level of an emergent research
front. In this Perspective we give an overview with a focus in connecting this
topic to others like Floquet systems. Furthermore, using a simple scattering
picture we discuss an interpretation of concepts like the Hamiltonian's
defectiveness, i.e. the lack of a full basis of eigenstates, crucial in many
discussions of topological phases of non-Hermitian Hamiltonians.
