Subwavelength apertures and holes on surfaces of metals induce strong electromagnetic field enhancement and extraordinary optical transmission. This remarkable phenomenon can lead to potentially significant applications in biological and chemical sensing, spectroscopy, and other novel optical devices. In this talk, I will present mathematical studies of the enhancement mechanism for the scattering of narrow slits in a slab of perfect conductor. Both the single slit and an array of slits will be discussed. It is demonstrated that the enhancement of the electromagnetic field for a single slit can be induced either by Fabry-Perot type scattering resonances or certain non-resonant effect in the low frequency. We derive the asymptotic expansions of resonances and quantitatively analyze the field enhancement at resonant frequencies. The field enhancement at non-resonant frequencies in the low frequency is also investigated, and it is shown that the fast transition of the magnetic field in the slit induces strong electric field enhancement. For a periodic array of slits, we show that additional enhancement mechanisms arise when the size of period changes.