  Here, we present an overview of a first principles homogenization theory of
periodic metamaterials. It is shown that in a rather general context it is
possible to formally introduce effective parameters that describe the time
evolution of macroscopic (slowly-varying in space) initial states of the
electromagnetic field using an effective medium formalism. The theory is
applied to different types of "wire metamaterials" characterized by a strong
spatial dispersion in the long wavelength limit. It is highlighted that the
spatial dispersion may tailor in unique ways the wave phenomena in wire
metamaterials leading to exotic tunneling effects and broadband lossless
anomalous dispersion.
