The so-called extraordinary optical transmission (EOT) through metallic nanoholes has triggered extensive research in modern plasmonics, due to its significant applications in imaging, bio-sensing, etc. The mechanisms contributing to the EOT phenomenon can be complicated due to the multiscale nature of the underlying structure. In this talk, I will focus on mechanisms induced by resonances. Based upon the layer potential technique, asymptotic analysis and the homogenization theory, rigorous mathematical analysis will be presented to investigate the scattering resonances for several two-dimensional structures, these include Fabry-Perot resonance, Fano resonance, spoof surface plasmon, etc.