  Non-Markovian local in time master equations give a relatively simple way to
describe the dynamics of open quantum systems with memory effects. Despite
their simple form, there are still many misunderstandings related to the
physical applicability and interpretation of these equations. Here we clarify
these issues both in the case of quantum and classical master equations. We
further introduce the concept of a classical non-Markov chain signified through
negative jump rates in the chain configuration.
