Isotopic compositions are referred to as anomalous if the isotopic ratios measured cannot be related to the terrestrial (solar) composition of a given element. While small effects close to the resolution of mass spectrometric techniques can have ambiguous origins, the discovery of large isotopic anomalies in inclusions and grains from primitive meteorites suggests that material from distinct sites of stellar nucleosynthesis has been preserved. Refractory inclusions, which are predominantly composed of the refractory oxides of Al, Ca, Ti, and Mg, in chondritic meteorites commonly have excesses in the heaviest isotopes of Ca, Ti, and Cr which are inferred to have been produced in a supernova. Refractory inclusions also contain excess 26Mg from short lived 26Al decay. However, despite the isotopic anomalies indicating the preservation of distinct nucleosynthetic sites, refractory inclusions have been processed in the solar system and are not interstellar grains. Carbon (graphite and diamond) and silicon carbide grains from the same meteorites also have large isotopic anomalies but these phases are not stable in the oxidized solar nebula which suggests that they are presolar and formed in the circumstellar atmospheres of carbon-rich stars. Diamond has a characteristic signature enriched in the lightest and heaviest isotopes of Xe, and graphite shows a wide range in C isotopic compositions. SiC commonly has C and N isotopic signatures which are characteristic of H-burning in the C-N-O cycle in low-mass stars. Heavier elements such as Si, Ti, Xe, Ba, and Nd, carry an isotopic signature of the s-process. A minor population of SiC (known as Grains X, ca. 1%) are distinct in having decay products of short lived isotopes 26Al (now 26Mg), 44Ti (now 44Ca), and 49V (now 49Ti), as well as 28Si excesses which are characteristic of supernova nucleosynthesis. The preservation of these isotopic anomalies allows the examination of detailed nucleosynthetic pathways in stars.