The low-lying dipole states, known as Pygmy Dipole Resonances (PDR) have been studied at length for several nuclei and several isotopes. Many properties have been acquired and understood by the theoretical and experimental studies of the isovector and isoscalar response of the PDR. Nevertheless, some unresolved questions still remain and two of them are briefly discussed in this contribution: the long standing question about the collective nature of this new mode and the presence of the PDR in deformed nuclei.