  We assert that the physics underlying the extraordinary light transmission
(reflection) in nanostructured materials can be understood from rather general
principles based on the formal scattering theory developed in quantum
mechanics. The Maxwell equations in passive (dispersive and absorptive) linear
media are written in the form of the Schr\"{o}dinger equation to which the
quantum mechanical resonant scattering theory (the Lippmann-Schwinger
formalism) is applied. It is demonstrated that the existence of long-lived
quasistationary eigenstates of the effective Hamiltonian for the Maxwell theory
naturally explains the extraordinary transmission properties observed in
various nanostructured materials. Such states correspond to quasistationary
electromagnetic modes trapped in the scattering structure. Our general approach
is also illustrated with an example of the zero-order transmission of the
TE-polarized light through a metal-dielectric grating structure. Here a direct
on-the-grid solution of the time-dependent Maxwell equations demonstrates the
significance of resonances (or trapped modes) for extraordinary light
transmissio
