One of the main ingredients of nuclear astrophysics is the cross section of the thermonuclear reactions which power the stars and synthesize the chemical elements in the Universe. Deep underground in the Gran Sasso Laboratory the cross section of the key reactions of the proton- proton chain and of the Carbon-Nitrogen-Oxygen (CNO) cycle have been measured right down to the energies of astrophysical interest. The main results obtained during the ’solar’ phase of LUNA are reviewed and their influence on our understanding of the properties of the neutrino and of the Sun is discussed. We then describe the current LUNA program devoted to the study of the nucleosynthesis of the light elements in AGB stars, Classical Novae and at the time of the big bang. Finally, the future of LUNA with the new 3.5 MV accelerator is outlined. This single-ended accelerator will be installed under Gran Sasso in spring 2018. It will provide hydrogen, helium and carbon (also doubly ionized) high current beams and it will be devoted to the study of helium and carbon burning in stars.