Microcavities and nanoresonators have the ability to strongly enhance many light−matter-interaction processes used in various applications in nano-optics. This enhancement is due to the resonant excitation of an electromagnetic mode that confines light in space (mode volume) and in time (quality factor). The confinement is not perfect and the modes, even dark ones, always leak some energy and have a finite lifetime. Their non-Hermitian character does significantly more than merely broadening the resonances. In this Perspective, we clarify the main difference between bound modes of Hermitian systems and leaky modes of non-Hermitian resonators, emphasizing the key existence of a spatially dependent phase factor as a signature of nonhermiticity. For decades, the phase factor has often be considered as puzzling or has even be ignored, although it plays a key role in the interpretation of many experiments on nanoscale resonant-mediated light−matter interaction, such as sensing with cavity perturbation, modification of the spontaneous emission rate, optomechanics, strong coupling, and so on. The situation has changed recently, to a point that nowadays a sound non-Hermitian formalism has been developed and freeware packages exist, helping analyze experiments that continuously push back the extraordinary limit offered by large fields for exploring matter with light.Read less <