  In this Review, the theory and applications of optical micro and
nanoresonators are presented from the underlying concept of their natural
resonances, the so-called quasi-normal modes (QNMs). The latter are the basic
constituents governing the response of resonators. Characterized by complex
frequencies, QNMs are initially loaded by a driving field and then decay
exponentially in time due to power leakage or absorption. Here, the use of
QNM-expansion formalisms to model these basic effects is explored. Such modal
expansions that operate at complex frequencies distinguish from the current
user habits in electromagnetic modeling, which rely on classical Maxwell
equation solvers operating at real frequencies or in the time domain; they also
bring much deeper physical insight into the analysis. An extensive overview of
the historical background on QNMs in electromagnetism and a detailed discussion
of recent relevant theoretical and numerical advances are therefore presented.
Additionally, a concise description of the role of QNMs on a number of examples
involving electromagnetic resonant fields and matter, including the interaction
between quantum emitters and resonators (Purcell effect, weak and strong
coupling, superradiance...), Fano interferences, the perturbation of resonance
modes, and light transport and localization in disordered media is provided.
