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Palladium is a prototypical hydride-forming metal, which can accommodate a large volume of hydrogen through the formation of either interstitial or complex hydrides. Interstitial palladium hydrides, especially those with exceptionally high hydrogen loadings, have attracted considerable interest from the low-energy nuclear reaction (LENR) community, as they have been invoked to explain the anomalous nuclear effects related to the known but controversial Pons-Fleischmann experiment. Complex palladium hydrides also constitute a class of solid-state hydrides that present stoichiometric PdH2, PdH3, or PdH4 units within the crystal structure, but remain unexplored as far as the unusual H/Pd ratio is concerned. This minireview gives a brief introduction to these two types of solid-state palladium hydrides, with the hope of providing some information for materials development relevant to LENR research.