Gamow-Teller (GT) transitions, aside from their interest from the nuclear structure point of view, play very important roles in various phenomena in nature. In nucleosynthesis, the b-decay of nuclei along the s- and r-processes determine 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 of giant stars. Electron capture is mediated by GT transitions. Electron capture 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 and leaving a neutron star or black hole behind. In 2n2b-decay, virtual GT transitions via 1⁺ states of the intermediate nucleus, determine the rate and therefore the lifetime of 2b-decaying nuclei. The 0n2b-decay is much more interesting since if it occurs it establishes the Majorana character of the neutrino and allows a determination of its mass. However, a good determination of the matrix element connecting both ground states is important. Here, in addition to GT transitions that are important in 2n2b-decay, higher multipolarity spin-isospin modes play an important role in determining this matrix element. Experimental aspects of this will be discussed