The composition of primary kimberlite melts and, in particular, the absolute and relative abundances of volatile components (mainly CO2 and H2O) are controversial issues, because kimberlite melts entrain and interact with abundant mantle and crustal xenoliths during ascent, react with wall rocks during emplacement, and lose some of their volatile inventory during pre- and syn-emplacement degassing. Compositional constraints are further complicated by the common alteration of kimberlitic rocks by post-emplacement fluids of various origin (e.g., deuteric, meteoric, hydrothermal). Consequently, the compositions of kimberlitic rocks may not be entirely representative of their parental melts. In kimberlitic rocks, CO2 is concentrated in carbonate minerals, whereas H2O is mainly stored in the secondary minerals serpentine and, to a lesser extent, chlorite and brucite, with minor contribution by primary magmatic phlogopite. This review focuses on utility of carbon, oxygen and sulphur stable isotopes to constrain the source of volatiles (i.e. magmatic vs non-magmatic) for carbonate, serpentine, sulphide and sulphate formation and the origin of fluids altering kimberlitic rocks.A global compilation of kimberlite carbonate data (δ13C=-11.9 to +0.2‰, median δ13C=-5.0‰, relative to VPDB; δ18O=1.2-26.6‰, median δ18O=13.2‰, relative to VSMOW) reveals that the majority of results (86%) plot within a range of δ13C~-2 to -8‰, which is considered representative of mantle carbon, but only 15% of analyses are in the field of oxygen isotopic values for mantle carbonates (δ18O~6-9‰). Variations in kimberlite carbon isotopic compositions occur on regional scales, implying widespread mantle heterogeneity, possibly related to input of carbon from recycled crustal material and/or partial overprinting by secondary processes at the local scale. Carbonates in southern African Group I (or archetype) and Group II kimberlites (or orangeites) show different δ13C distributions (median values of -5.3‰ and -6.5‰, respectively). This is consistent with distinct mantle sources, as demonstrated previously by radiogenic isotope studies. Kimberlite breccia carbonates commonly have higher δ18O values than carbonates in massive and hypabyssal kimberlites, which suggests more extensive interaction of kimberlite rocks with hydrous fluids in the brecciated parts of kimberlite pipes. Modelling of the stable isotope compositions of carbonates from the Kimberley, Lac de Gras and Udachnaya-East kimberlites reveals that several processes are capable of modifying these compositions, including interaction with H2O-rich deuteric (i.e. late-stage magmatic) fluids, meteoric waters and/or hydrothermal fluids, and incorporation of sedimentary material. However, these processes can produce similar variations of the carbonate C-O isotopic compositions, which means that carbonate isotopes alone cannot provide tight constraints on the alteration of kimberlite rocks. Only few carbonates in hypabyssal kimberlites show isotopic compositions consistent with abundant CO2 degassing (i.e. increasing δ18O with decreasing δ13C values), thus implying that kimberlite magmas that are not emplaced explosively retain most of their CO2 concentrations prior to carbonate crystallisation.In kimberlitic rocks early-formed serpentine exhibits higher δ18O values (~+4-+6‰) than later serpentine rims and segregations (δ18O values as low as ~-2‰). These variations are consistent with serpentine crystallisation from hydrous fluids derived from mixing between deuteric fluids and meteoric/hydrothermal fluids, with progressive enrichment in the latter component. Serpentine is considered to have formed under hydrothermal conditions when externally derived hydrous fluids infiltrated the cooling kimberlite volcanic system.Only limited sulphur isotopic data are available for kimberlitic bulk rocks and sulphide and sulphate phases. Of these, relatively few sulphur isotopic ratios approach the δ34S values considered representative of the mantle (0±2‰, relative to VCDT). Elevated δ34S values (~14‰) characteristic of sulphates in the Udachnaya-East kimberlite are consistent with equilibration with sulphides (δ34S~1-2‰) at temperatures of ~500-550°C, after kimberlite melt outgassing under oxidising conditions. Conversely, the large δ34S range shown by some southern African and Yakutian kimberlites (-3-+12‰ and +15-+53‰, respectively) may be largely due to alteration and crustal contamination.In conclusion, the stable isotopic compositions of carbonates, serpentine and S-rich minerals in kimberlites, can be used in conjunction with detailed petrographic and geochemical analyses, to constrain processes affecting kimberlite magmas prior to, during, and subsequent to crystallisation. The available stable isotopic data indicate that externally derived (i.e. non-magmatic) hydrothermal fluids have affected the compositions of most kimberlites, including the hypabyssal varieties often used to reconstruct the compositions of primary kimberlite melts. This discrepancy remains a major obstacle in the quest for the primary composition of kimberlite melts. © 2014 Elsevier B.V.