  The engineering of the spatial and temporal properties of both the electric
permittivity and the refractive index of materials is at the core of photonics.
When vanishing to zero, those two variables provide new knobs to control
light-matter interactions. This perspective aims at providing an overview of
the state of the art and the challenges in emerging research areas where the
use of near-zero refractive index and hyperbolic metamaterials is pivotal, in
particular light and thermal emission, nonlinear optics, sensing applications
and time-varying photonics.
