This paper reviews the chemical processes responsible for fractionating deuterium in interstellar molecules. I show that this process is intrinsically a low temperature phenomenon and discuss how the degree of enhancement of the deuterium content of molecules is related to the physical conditions, particularly abundances, in molecular clouds. If significant amounts of abundant species, such as CO, are frozen out on to interstellar dust grains, the resulting enhancement in H2D+ can result in its abundance being greater than that of H3 + at 10 K. Transfer of the deuteron from H2D+ can then lead to the efficient formation of multiply deuterated species, such as NHD2 and ND3. Fractionation can also occur in grain surface reactions and some simple models are discussed.