The beta-decay of Ca-37 has been studied. The half-life was remeasured with improved precision to be 181.1+/-1.0 ms, and beta-delayed gamma-rays were observed for the first time. The surprisingly high Gamma(g)amma/Gamma(p) values for proton-unbound states in K-37 drastically reduce former discrepancies between the Gamow-Teller strength values B(GT) measured in the Ca-37 beta-decay and those deduced from the Cl-37(p,n)Ar-37 mirror reaction.