  Electromagnetic cavity modes in photonic and plasmonic resonators offer rich
and attractive regimes for tailoring the properties of light-matter
interactions. Yet there is a disturbing lack of a precise definition for what
constitutes a cavity mode, and as a result their mathematical properties remain
largely unspecified. The lack of a definition is evidenced in part by the
diverse nomenclature at use - "resonance", "leaky mode", "quasimode", to name
but a few - suggesting that the dissipative nature of cavity modes somehow
makes them different from other modes, but an explicit distinction is rarely
made. This perspective article aims to introduce the reader to some of the
subtleties and working definitions that can be rigorously applied when
describing the modal properties of leaky optical cavities and plasmonic
nanoresonators. We describe some recent development in the field, including
{calculation methods for quasinormal modes of both photonic and plasmonic
resonators and the concept of a generalized effective mode volume, and we}
illustrate the theory with several representative cavity structures from the
fields of photonic crystals and nanoplasmonics.
