Deuterium fractionations in cometary ices provide important clues to the origin and evolution of comets. Mass spectrometers aboard spaceprobe Giotto revealed the first accurate D/H ratios in the water of Comet 1P/Halley. Ground-based observations of HDO in Comets C/1996 B2 (Hyakutake) and C/1995 O1 (Hale-Bopp), the detection of DCN in Comet Hale-Bopp, and upper limits for several other D-bearing molecules complement our limited sample of D/H measurements. On the basis of this data set all Oort cloud comets seem to exhibit a similar (D/H)H2O ratio in H2O, enriched by about a factor of two relative to terrestrial water and approximately one order of magnitude relative to the protosolar value. Oort cloud comets, and by inference also classical short-period comets derived from the Kuiper Belt cannot be the only source for the Earth's oceans. The cometary O/C ratio and dynamical reasons make it difficult to defend an early influx of icy planetesimals from the Jupiter zone to the early Earth. D/H measurements of OH groups in phyllosilicate rich meteorites suggest a mixture of cometary water and water adsorbed from the nebula by the rocky grains that formed the bulk of the Earth may be responsible for the terrestrial D/H. The D/H ratio in cometary HCN is 7 times higher than the value in cometary H2O. Species-dependent D-fractionations occur at low temperatures and low gas densities via ion-molecule or grain-surface reactions and cannot be explained by a pure solar nebula chemistry. It is plausible that cometary volatiles preserved the interstellar D fractionation. The observed D abundances set a lower limit to the formation temperature of (30 +/- 10) K. Similar numbers can he derived from the ortho-to-para ratio in cometary water, from the absence of neon in cometary ices and the presence of S2. Noble gases on Earth and Mars, and the relative abundance of cometary hydrocarbons place the comet formation temperature near 50 K. So far all cometary D/H measurements refer to bulk compositions, and it is conceivable that significant departures from the mean value could occur at the grain-size level. Strong isotope effects as a result of coma chemistry can be excluded for molecules H2O and HCN. A comparison of the cometary (D/H)H2O ratio with values found in the atmospheres of the outer planets is consistent with the long-held idea that the gas planets formed around icy cores with a high cometary D/H ratio and subsequently accumulated significant amounts of H2 from the solar nebula with a low protosolar D/H.