SPI on INTEGRAL has provided spectra and a map of the sky in the emission from annihilations of positrons in the interstellar medium of our Galaxy. From high-resolution spectra we learned that a warm, partially-ionized medium is the site where the observed gamma-rays originate. The gamma-ray emission map shows a major puzzle for broader astrophysics topics, as it is dominated by a bright and extended apparently spherical emission region centered in the Galaxys center. Only recently has the disk of the Galaxy been detected with SPI. This may be regarded as confirmation of earlier expectations that positrons should arise predominantly from sources of nucleosynthesis distributed throughout the plane of the Galaxy, which produce proton-rich unstable isotopes. But there are other plausible sources of positrons, among them pulsars and accreting binaries such as microquasars. SPI results may be interpreted also as hints that these are more significant as positron sources on the Galactic scale than thought before, in the plane and therefore also in the bulge of the Galaxy. This is part of the attempt to understand the surprisingly-bright emission from the central region in the Galaxy, which otherwise also could be interpreted as a first rather direct detection of dark matter annihilations in the Galaxys gravitational well. INTEGRAL has a unique potential to shed light on the various aspects of positron astrophysics, through its capability for imaging spectroscopy.