We review progress in studying two central problems in Nuclear Astrophysics: The \be7pg reaction is one of the major source of uncertainties in estimating the \b8 solar neutrino flux and is critical for the Solar Neutrino Problem. We discuss a newly emerging method to extract this cross section from the Coulomb dissociation of the radioactive beam of \b8. The Coulomb dissociation appears to provide a viable alternative method for measuring the \be7pg reaction rate. Several attempts to constrain the p-wave S-factor of the \c12ag reaction at Helium burning temperatures (200 MK) using the beta-delayed alpha-particle emission of \n16 have been made, and it is claimed that this S-factor is known, as quoted by the TRIUMF collaboration. In contrast reanalyses (by G.M. hale) of all thus far available data (including the \n16 data) does not rule out a small S-factor solution. Furthermore, we improved our previous Yale-UConn study of the beta-delayed alpha-particle emission of \n16. Our newly measured spectrum of the beta-delayed alpha-particle emission of \n16 is not consistent with the TRIUMF('94) data, but is consistent with the Seattle('95) data, as well as the earlier (unaltered !) data of Mainz('71). The implication of this discrepancies for the extracted astrophysical p-wave s-factor is briefly discussed.