Measurements of the chemical composition of the giant planets provide clues of their formation and evolution processes. According to the currently accepted nucleation model, giant planets formed from the initial accretion of all icy core and the capture of the protosolar gas, mosly composed of hydrogen and helium. In the case of Jupiter and Saturn (the gaseous giants), this gaseous component dominates the composition of the planet, while for Uranus and Neptune (the icy giants) it is only a small fraction of the total mass. The measurement of elemental and isotopic ratios in the giant planets provides key diagnostics of this model, as it implies an enrichment in heavy elements (as well as deuterium) with respect to the cosmic composition. Neutral atmospheric constituents in the giant planets have three possible sources: (1) internal (from the bulk composition of the planet), (2) photochemical (from the photolysis of methane) and (3) external (from meteoritic impacts, of local or interplanetary origin). This paper reviews our present knowledge about the atmospheric composition in the giant planets, and their elemental and istopic composition. Measurements concerning key parameters, like C/H, D/H or rare gases in Jupiter, are analysed in detail. The conclusion addresses open questions and observations to be performed in the future.