  An important issue in phenomenological macroscopic electrodynamics of moving
media is the definition of the energy and momentum of the electromagnetic field
in matter. Rather surprisingly, this topic has demonstrated a remarkable
longevity, and the problem of the electromagnetic energy and momentum in matter
remained open, despite numerous theoretical and experimental investigations. We
overview the definition of the momentum of light in matter and demonstrate
that, for the correct understanding of the problem, one needs to carefully
distinguish situations when the material medium is modeled either as a
background for light or as a dynamical part of the total system. The status of
Minkowski and Abraham energy-momentum tensors of the electromagnetic field is
clarified for the two particular types of complex matter, the spinning fluid
and the liquid crystal medium, and summarized for the case of general
anisotropic moving material media with a linear constitutive law.
