  This article reviews the material properties that enable maximum optical
response. We highlight theoretical results that enable shape-independent
quantification of material "figures of merit," ranging from classical sum rules
to more recent single-frequency scattering bounds. A key delineation at optical
frequencies is between polaritonic materials that support highly subwavelength
resonances and dielectric materials that can have vanishingly small loss rates.
We discuss the key metrics that enable comparisons both within these material
classes and between them. We discuss analogous metrics for 2D materials, and
point to applications for which rigorous comparison can be made between bulk-
and 2D-material approaches. The various results highlight the synergy between
materials discovery and theoretical nanophotonic bounds, and point to
opportunities in achieving new extremes in light--matter interactions.
