  In this review we look at the concepts and state-of-the-art concerning the
strong coupling of surface plasmon-polariton modes to states associated with
quantum emitters such as excitons in J-aggregates, dye molecules and quantum
dots. We explore the phenomenon of strong coupling with reference to a number
of examples involving electromagnetic fields and matter. We then provide a
concise description of the relevant background physics of surface plasmon
polaritons. An extensive overview of the historical background and a detailed
discussion of more recent relevant experimental advances concerning strong
coupling between surface plasmon polaritons and quantum emitters is then
presented. Three conceptual frameworks are then discussed and compared in
depth: classical, semi-classical and fully quantum mechanical; these
theoretical frameworks will have relevance to strong coupling beyond that
involving surface plasmon polaritons. We conclude our review with a perspective
on the future of this rapidly emerging field, one we are sure will grow to
encompass more intriguing physics and will develop in scope to be of relevance
to other areas of science.
