  Open quantum systems (OQS) cannot always be described with the Markov
approximation, which requires a large separation of system and environment time
scales. Here, we give an overview of some of the most important techniques
available to tackle the dynamics of an OQS beyond the Markov approximation.
Some of these techniques, such as master equations, Heisenberg equations and
stochastic methods, are based on solving the reduced OQS dynamics, while
others, such as path integral Monte Carlo or chain mapping approaches, are
based on solving the dynamics of the full system. We emphasize the physical
interpretation and derivation of the various approaches, explore how they are
connected and examine how different methods may be suitable for solving
different problems.

Quantum Physics