LUNA (Laboratory for Underground Nuclear Astrophysics) is a nuclear astrophysics experiment running at the INFN Laboratori Nazionali del Gran Sasso (LNGS). Aim of the experiment is to measure the crosssection of fusion reactions that take place inside the stars and that, in the past, dominated the Big Bang nucleosynthesis (BBN). The low value of these cross-sections (varying from pb to fb and even smaller), in the astrophysical range of energies, prevent any kind of measurements at the Earth's surface. On the other hand, the low background of the LNGS underground laboratory allows LUNA to investigate these reactions at energies of astrophysical interest without the necessity of an extrapolation from the highest energies. Recently, the LUNA Collaboration has been engaged in the study of the ²H(α, γ)6Li and 17O(p, γ)18F reactions. In this paper the experimental set-up will be described and the preliminary data will be discussed. The future possibilities of LUNA will also be outlined. [ABSTRACT FROM AUTHOR]