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The recent extensions of the covariant energy density functional theory withthe quasiparticle-vibration coupling (QVC) are reviewed. Formulation of theQuasiparticle Random Phase Approximation (QRPA) in the relativistic frameworkis discussed. Self-consistent extensions of the relativistic QRPA imply the QVCwhich is implemented in two-body propagators in the nuclear medium. Thisprovides fragmentation of the QRPA states describing the damping of thevibrational motion.

Microscopic description of nuclear vibrations: Relativistic QRPA and its extensions with quasiparticle-vibration coupling