Since the discovery of the extraordinary optical transmission through nanohole arrays in metallic films by Ebbesen, a wealth of research has been sparked in the experimental and theoretical investigation of localized electromagnetic field enhancement in subwavelength nanostructures. This remarkable phenomenon can lead to potentially significant applications in near-field imaging, biosensing, etc. However, there has been a long debate on the interpretation of the enhancement effect since Ebbesen’s work. In addition, a quantitative analysis of the field enhancement in subwavelength structures is still widely open. In this talk, using two-dimensional slits as a prototype, I will present mathematical studies of the field enhancement in the subwavlength structures. 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 resonances or certain non-resonant effect at low frequencies. For a periodic array of slits, several different enhancement mechanisms would arise if the scaling between the size of the slit, the size of the period, and the wavelength of the incident wave varies. The asymptotics for the enhanced electromagnetic fields will also be derived for both structures. The study is a first step toward the understanding of the enormous enhancement that occurs in a rich collection of nanostructures, and the ongoing exploration along this direction will be highlighted.