  This review provides a brief introduction to the physics of coupled
exciton-plasmon systems, the theoretical description and experimental
manifestation of such phenomena, followed by an account of the state-of-the-art
methodology for the numerical simulations of such phenomena and supplemented by
a number of FORTRAN codes, by which the interested reader can introduce
himself/herself to the practice of such simulations. Applications to CW light
scattering as well as transient response and relaxation are described.
Particular attention is given to so-called strong coupling limit, where the
hybrid exciton-plasmon nature of the system response is strongly expressed.
While traditional descriptions of such phenomena usually rely on analysis of
the electromagnetic response of inhomogeneous dielectric environments that
individually support plasmon and exciton excitations, here we explore also the
consequences of a more detailed description of the molecular environment in
terms of its quantum density matrix (applied in a mean field approximation
level). Such a description makes it possible to account for characteristics
that cannot be described by the dielectric response model: the effects of
dephasing on the molecular response on one hand, and nonlinear response on the
other. It also highlights the still missing important ingredients in the
numerical approach, in particular its limitation to a classical description of
the radiation field and its reliance on a mean field description of the
many-body molecular system. We end our review with an outlook to the near
future, where these limitations will be addressed and new novel applications of
the numerical approach will be pursued.
