  We investigate the dynamics of quantum correlations (QC) under the effects of
reservoir memory, as a resource for quantum information and computation tasks.
Quantum correlations of two-qubit systems are used for implementing quantum
teleportation successfully, and for investigating how teleportation fidelity,
violation of Bell-CHSH inequality, quantum steering and entanglement are
connected with each other under the influence of noisy environments. Both
Markovian and non-Markovian channels are considered, and it is shown that the
decay and revival of correlations follow the hierarchy of quantum correlations
in the state space. Noise tolerance of quantum correlations are checked for
different types of unital and non-unital quantum channels, with and without
memory. The quantum speed limit time $(\tau_{QSL})$ is investigated from the
perspective of memory of quantum noise, and the corresponding dynamics is used
to analyze the evolution of quantum correlations. We establish the connection
between information backflow, quantum speed limit time and dynamics of quantum
correlations for non-Markovian quantum channels.
