The results of electronic structure calculations for a variety of palladium hydrides are presented. The calculations are based on density functional theory and used different local and semilocal approximations. The thermodynamic stability of all structures as well as the electronic and chemical bonding properties are addressed. For the monohydride, taking into account the zero-point energy is important to identify the octahedral Pd-H arrangement with its larger voids and, hence, softer hydrogen vibrational modes as favorable over the tetrahedral arrangement as found in the zincblende and wurtzite structures. Stabilization of the rocksalt structure is due to strong bonding of the 4d and 1s orbitals, which form a characteristic split-off band separated from the main d-band group. Increased filling of the formerly pure d states of the metal causes strong reduction of the density of states at the Fermi energy, which undermines possible long-range ferromagnetic order otherwise favored by strong magnetovolume effects. For the dihydride, octahedral Pd-H arrangement as realized e.g. in the pyrite structure turns out to be unstable against tetrahedral arrangement as found in the fluorite structure. Yet, from both heat of formation and chemical bonding considerations the dihydride turns out to be less favorable than the monohydride. Finally, the vacancy ordered defect phase Pd3H4 follows the general trend of favouring the octahedral arrangement of the rocksalt structure for Pd:H ratios less or equal to one.Read less <