  The last two decades have seen major developments in interpolatory methods
for model reduction of large-scale linear dynamical systems. Advances of note
include the ability to produce (locally) optimal reduced models at modest cost;
refined methods for deriving interpolatory reduced models directly from
input/output measurements; and extensions for the reduction of parametrized
systems. This chapter offers a survey of interpolatory model reduction methods
starting from basic principles and ranging up through recent developments that
include weighted model reduction and structure-preserving methods based on
generalized coprime representations. Our discussion is supported by an
assortment of numerical examples.
