  Static metasurfaces have shown to be prominent compact structures for
reciprocal and frequency-invariant transformation of electromagnetic waves in
space. However, incorporating temporal variation to static metasurfaces would
result in dynamic apparatuses which are capable of four-dimensional tailoring
of both the spatial and temporal characteristics of electromagnetic waves,
leading to functionalities that are far beyond the capabilities of conventional
static metasurfaces. This includes nonreciprocal full-duplex wave transmission,
pure frequency conversion, parametric wave amplification, spatiotemporal
decomposition, and space-time wave diffraction. This paper reviews recent
progress and opportunities offered by space-time metasurfaces to break
reciprocity, revealing their potential for low-energy, compact, integrated
non-reciprocal devices and sub-systems, and discusses the future of this
exciting research front.
