He was one of the many world-class German physicists who left when the Nazis came to power. Like many of them, he worked on the Manhattan Project; indeed, Bethe headed up the theoretical division. His Nobel Prize was awarded for his work on explaining the fusion process that fuels stars. He was also responsible for explaining the Lamb Shift, a development that led to modern quantum field theories, specifically quantum electrodynamics (QED).
But he will be best remembered for the legendary paper (Physical Review - April 1st, 1948) co-authored with George Gamow and Ralph Alpher that provided mathematical details of Big Bang nucleosynthesis. Bethe didn’t actually contribute anything, but Gamow insisted that the paper be bylined Alpher-Bethe-Gamow.