Particle-phonon coupling: Understanding the variety of excitations in the low-lying spectra of odd nuclei

The couplings between particles and vibrations in atomic nuclei play a key role in the understanding of various nuclear properties, as it has been highlighted along several decades. In this contribution, after a short survey of the early discoveries of particle-phonon multiplets around the Pb-208 region, we review recent experiments and theoretical attempts to understand low-energy spectra of odd-nuclei close to magic and semi-magic cores, where particle-phonon coupling phenomena play a significant role. The focus will be on nuclei around Ca-48 , Sn-132 , Pb-208 and neutron-rich Ni isotopes. Special emphasis will be given to experimental techniques based on high-resolution gamma-spectroscopy and to recent theoretical developments aimed at disentangling particle-phonon coupled states and other more hybrid configurations, using the Hybrid Configuration Mixing model that has been recently proposed by the Milano group.