The behavior of hydrogen in metals has attracted considerable attention in fundamental and applied research areas for many decades. Among metals, palladium is remarkable because it can absorb large quantities of hydrogen, and hydrogen atoms are highly mobile in the fcc Pd lattice. The dynamics of hydrogen in Pd have been investigated by neutron spectroscopy, which is the best tool to provide insights into the microscopic dynamics of hydrogen atoms. As for a bulk system, the phonon dispersion relations and atomic vibrations of hydrogen were successfully measured by inelastic neutron scattering. The jump diffusion processes among interstitial sites Pd lattices were also confirmed by quasielastic neutron scattering. The above observations were reconciled with theoretical calculations... incorporating quantum effects. The nanoparticles and deformed materials, in which the environment surrounding hydrogen is significantly changed, were also investigated. Non-bulk-like behaviors indicate the existence of new stable sites generated in the modified environment. In this article, we review recent and historical neutron scattering works to facilitate the latest understanding of the hydrogen dynamics in bulk and nanometer-sized Pd hydrides.