  In the recent decades, it became more and more popular for engineers,
physicists, and mathematicians alike to put the Maxwell equations into a
generally covariant form. This is particularly useful for understanding the
fundamental structure of electrodynamics (conservation of electric charge and
magnetic flux). Moreover, it is ideally suited for applying it to media with
local (and mainly linear) response behavior. We try to collect the new
knowledge that grew out of this development. We would like to ask the
participants of EMTS 2016 to inform us of work that we may have overlooked in
our review.
