  The essential ingredients of nuclear astrophysics are the thermonuclear
reactions which shape the life and death of stars and which are responsible for
the synthesis of the chemical elements in the Universe. Deep underground in the
Gran Sasso Laboratory the cross sections of the key reactions responsible for
the hydrogen burning in stars have been measured with two accelerators of 50
and 400 kV voltage right down to the energies of astrophysical interest. As a
matter of fact, the main advantage of the underground laboratory is the
reduction of the background. Such a reduction has allowed, for the first time,
to measure relevant cross sections at the Gamow energy. The qualifying features
of underground nuclear astrophysics are exhaustively reviewed before discussing
the current LUNA program which is mainly devoted to the study of the Big-Bang
nucleosynthesis and of the synthesis of the light elements in AGB stars and
classical novae. The main results obtained during the study of reactions
relevant to the Sun are also reviewed and their influence on our understanding
of the properties of the neutrino, of the Sun and of the Universe itself is
discussed. Finally, the future of LUNA during the next decade is outlined. It
will be mainly focused on the study of the nuclear burning stages after
hydrogen burning: helium and carbon burning. All this will be accomplished
thanks to a new 3.5 MV accelerator able to deliver high current beams of
proton, helium and carbon which will start running under Gran Sasso in 2019. In
particular, we will discuss the first phase of the scientific case of the 3.5
MV accelerator focused on the study of $^{12}$C+$^{12}$C and of the two
reactions which generate free neutrons inside stars:
$^{13}$C($\alpha$,n)$^{16}$O and $^{22}$Ne($\alpha$,n)$^{25}$Mg.
