  Near-field optics is an exciting frontier of photonics and plasmonics. The
tandem of strongly localized fields and enhanced emission rates offers
significant opportunities for wide-ranging applications, while also creating
basic questions: How large can such enhancements be? To what extent do material
losses inhibit optimal response? Over what bandwidths can these effects be
sustained? This chapter surveys theoretical techniques for answering these
questions. We start with physical intuition and mathematical definitions of the
response functions of interest (LDOS, CDOS, SERS, NFRHT, etc.), after which we
describe the general theoretical techniques for bounding such functions.
Finally, we apply those techniques specifically to near-field optics, for which
we describe known bounds, optimal designs, and open questions.
