  At visible and infrared frequencies, metals show tantalizing promise for
strong subwavelength resonances, but material loss typically dampens the
response. We derive fundamental limits to the optical response of absorptive
systems, bounding the largest enhancements possible given intrinsic material
losses. Through basic conservation-of-energy principles, we derive
geometry-independent limits to per-volume absorption and scattering rates, and
to local-density-of-states enhancements that represent the power radiated or
expended by a dipole near a material body. We provide examples of structures
that approach our absorption and scattering limits at any frequency, by
contrast, we find that common "antenna" structures fall far short of our
radiative LDOS bounds, suggesting the possibility for significant further
improvement. Underlying the limits is a simple metric, $|\chi|^2 /
\operatorname{Im} \chi$ for a material with susceptibility $\chi$, that enables
broad technological evaluation of lossy materials across optical frequencies.
