The study of giant resonances has been very fruitful in understanding the structure of these modes of excitation of the nucleus and also in helping to shed light onto certain astrophysical phenomena. For example, the compression modes, the isoscalar giant monopole (ISGMR) and dipole (ISGDR) resonances, were extensively studied because of their importance for the determination of the nuclear matter incompressibility and consequently their implications for the equation of state (EoS) of nuclear matter. Gamow-Teller (GT) transitions, on the other hand, play very important roles in various phenomena in nature. In nucleosynthesis, the β-decay of nuclei in the s- and r-processes determines the paths that these processes follow and the abundances of the elements synthesized. In supernova collisions, GT transitions are of paramount importance in the pre-supernova phase where electron capture occurs on neutron-rich fp-shell nuclei at the high temperatures reached in giant stars. Electron capture, which is mediated by GT transitions, removes the electron pressure that keeps the star from collapsing precipitating a cataclysmic implosion followed by a huge explosion throwing much of the star material into space leaving a neutron star or black hole behind.