Nuclear physics has a long and productive history of application to astrophysics which continues today. Advances in the accuracy and breadth of astrophysical data and theory drive the need for better experimental and theoretical understanding of the underlying nuclear physics. This paper will review some of the scenarios where nuclear physics plays an important role, including Big Bang Nucleosynthesis, neutrino production by our sun, nucleosynthesis in novae, the creation of elements heavier than iron, and neutron stars. Big-bang nucleosynthesis is concerned with the formation of elements with A <= 7 in the early Universe; the primary nuclear physics inputs required are few-nucleon reaction cross sections. The nucleosynthesis of heavier elements involves a variety of proton-, alpha-, neutron-, and photon-induced reactions, coupled with radioactive decay. The advent of radioactive ion beam facilities has opened an important new avenue for studying these processes, as many involve radioactive species. Nuclear physics also plays an important role in neutron stars: both the nuclear equation of state and cooling processes involving neutrino emission play a very important role. Recent developments and also the interplay between nuclear physics and astrophysics will be highlighted.