Synthesis of the elements in stars: forty years of progress

Forty years ago Burbidge, Burbidge, Fowler, and Hoyle combined what we would now call fragmentary evidence from nuclear physics, stellar evolution and the abundances of elements and isotopes in the solar system as well as a few stars into a synthesis of remarkable ingenuity. Their review provided a foundation for forty years of research in all of the aspects of low energy nuclear experiments and theory, stellar modeling over a wide range of mass and composition, and abundance studies of many hundreds of stars, many of which have shown distinct evidence of the processes suggested by B${}^{2}$FH. In this review we summarize progress in each of these fields with emphasis on the most recent developments.