  Knowledge of the dynamical behavior of correlations with no classical
counterpart, like entanglement, nonlocal correlations and quantum discord, in
open quantum systems is of primary interest because of the possibility to
exploit these correlations for quantum information tasks. Here we review some
of the most recent results on the dynamics of correlations in bipartite systems
embedded in non-Markovian environments that, with their memory effects,
influence in a relevant way the system dynamics and appear to be more
fundamental than the Markovian ones for practical purposes. Firstly, we review
the phenomenon of entanglement revivals in a two-qubit system for both
independent environments and a common environment. We then consider the
dynamics of quantum discord in non-Markovian dephasing channel and briefly
discuss the occurrence of revivals of quantum correlations in classical
environments.
