  A longstanding tool to characterize the evolution of open Markovian quantum
systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation.
However, in some cases, open quantum systems can be effectively described with
non-Hermitian Hamiltonians, which have attracted great interest in the last
twenty years due to a number of unconventional properties, such as the
appearance of exceptional points. Here, we present a short review of these two
different approaches aiming in particular to highlight their relation and
illustrate different ways of connecting non-Hermitian Hamiltonian to a GKSL
master equation for the full density matrix.
