Since its launch in October 2002, ESA's INTEGRAL observatory has enabled significant advances to be made in the study of Galactic nucleosynthesis. In particular, the imaging Ge spectrometer SPI combines for the first time the diagnostic powers of high resolution gamma-ray line spectroscopy and moderate spatial resolution. This review summarizes the major nucleosynthesis results obtained with INTEGRAL so far. Positron annihilation in our Galaxy is being studied in unprecented detail. SPI observations yield the first sky maps in both the 511 keV annihilation line and the positronium continuum emission, and the most accurate spectrum at 511 keV to date, thereby imposing new constraints on the source(s) of Galactic positrons which still remain(s) unidentified. For the first time, the imprint of Galactic rotation on the centroid and shape of the 1809 keV gamma-ray line due to the decay of $^{26}$Al has been seen, confirming the Galactic origin of this emission. SPI also provided the most accurate determination of the gamma-ray line flux due to the decay of $^{60}$Fe. The combined results for $^{26}$Al and $^{60}$Fe have important implications for nucleosynthesis in massive stars, in particular Wolf-Rayet stars. Both IBIS and SPI are searching the Galactic plane for young supernova remnants emitting the gamma-ray lines associated with radioactive $^{44}$Ti. None have been found so far, which raises important questions concerning the production of $^{44}$Ti in supernovae, the Galactic supernova rate, and the Galaxy's chemical evolution.