  Time-varying media have recently emerged as a new paradigm for wave
manipulation, thanks to thesynergy between the discovery of novel, highly
nonlinear materials, such as epsilon-near-zero materials, and the questfor
novel wave applications, such as magnet-free nonreciprocity, multi-mode light
shaping, and ultrafast switching. Inthis review we provide a comprehensive
discussion of the recent progress achieved with photonic metamaterials
whoseproperties stem from their modulation in time. We review the basic
concepts underpinning temporal switching and itsrelation with spatial
scattering, and deploy the resulting insight to review photonic time-crystals
and their emergentresearch avenues such as topological and non-Hermitian
physics. We then extend our discussion to account for spa-tiotemporal
modulation and its applications to nonreciprocity, synthetic motion, giant
anisotropy, amplification andother effects. Finally, we conclude with a review
of the most attractive experimental avenues recently demonstrated,and provide a
few perspectives on emerging trends for future implementations of
time-modulation in photonics.
