  Time-varying media break temporal symmetries while preserving spatial
symmetries intact. Thus, it represents an excellent conceptual framework to
investigate the fundamental implications of Noether's theorem for the
electromagnetic field. At the same time, addressing momentum conservation in
time-varying media sheds light on the Abraham-Minkowski debate, where two
opposing forms of the electromagnetic field momentum are defended. Here, we
present a tutorial review on the conservation of momentum in time-varying
media. We demonstrate that the Minkowski momentum is a conserved quantity with
three independent approaches of increasing complexity: (i) via the application
of the boundary conditions for Maxwell equations at a temporal boundary, (ii)
testing for constants of motion and deriving conservation laws, and (iii)
applying temporal and spatial translations within the framework of the
Lagrangian theory of the electromagnetic field. Each approach provides a
different and complementary insight into the problem.
