Meteorites and interplanetary dust particles contain presolar stardust grains: solid samples of stars that can be studied in the laboratory. The stellar origin of the grains is indicated by enormous isotopic ratio variations compared with Solar System materials, explainable only by nuclear reactions occurring in stars. Known presolar phases include diamond, SiC, graphite, Si3N4, Al2O3, MgAl2O4, CaAl12O19, TiO2, Mg(Cr,Al)2O4, and most recently, silicates. Subgrains of refractory carbides (e.g., TiC), and Fe-Ni metal have also been observed within individual presolar graphite grains. We review the astrophysical implications of these grains for the sciences of nucleosynthesis, stellar evolution, grain condensation, and the chemical and dynamic evolution of the Galaxy. Unique scientific information derives primarily from the high precision (in some cases <1%) of the measured isotopic ratios of large numbers of elements in single stardust grains. Stardust science is just now reaching maturity and will play an increasingly important role in nucleosynthesis applications.