Recent high-resolution experiments using electron and proton scattering and charge-exchange reactions covering a wide mass range of nuclei establish the fine structure of giant resonances as a global phenomenon. Experimental evidence includes a systematic study of the isoscalar giant quadrupole resonance (ISGQR) in 58Ni, 89Y, 90Zr, 120Sn and 208Pb, the first observation of fine structure of the Gamow-Teller resonance in a heavy nucleus, 90Nb, as well as of the isovector giant dipole (IVGDR) and magnetic quadrupole (M2) modes. Novel methods based on wavelet transforms are introduced for the extraction of scales characterizing the fine structure and evaluating their relative importance. Comparison of those scales to predictions from microscopic model calculations including 2p-2h degrees of freedom indicate surface vibration coupling as the underlying mechanism for their appearance. A generic pattern is also found for the stochastic coupling to the background of the more complex states.