In this chapter, we intend to explore and review some remarkable dynamical
properties of quantum discord under various different open quantum system
models. Specifically, our discussion will include several concepts connected to
the phenomena of time invariant and frozen quantum discord. Furthermore, we
will elaborate on the relation of these two phenomena to the non-Markovian
features of the open system dynamics and to the usage of dynamical decoupling
protocols.Comment: 29 pages, 8 figure