  The rapid development of metasurfaces - 2D ensembles of engineered
nanostructures - is presently fostering a steady drive towards the
miniaturization of many optical functionalities and devices to a subwavelength
size. The material platforms for optical metasurfaces are rapidly expanding and
for the past few years, we are seeing a surge in establishing meta-optical
elements from high-index, highly transparent materials with strong nonlinear
and electro-optic properties. Crystalline lithium niobate (LN), a prime
material of choice in integrated photonics, has shown great promise for future
meta-optical components, thanks to its large electro-optical coefficient,
second-order nonlinear response and broad transparency window ranging from the
visible to the mid-infrared. Recent advances in nanofabrication technology have
indeed marked a new milestone in the miniaturization of LN platforms, hence
enabling the first demonstrations of LN-based metasurfaces. These seminal works
set the first steppingstone towards the realization of ultra-flat monolithic
nonlinear light sources with emission ranging from the visible to the infrared,
efficient sources of correlated photon pairs, as well as electro-optical
devices. Here, we review these recent advances, discussing potential
perspectives for applications in light conversion and modulation shaping as
well as quantum optics, with a critical eye on the potential setbacks and
limitations of this emerging field.
