We present a simple and unified classification of macroscopic electromagnetic resonances in finite arbitrarily inhomogeneous isotropic dielectric 3D structures situated in free space. By observing the complex-plane dynamics of the spatial spectrum of the volume integral operator as a function of angular frequency and constitutive parameters, we identify and generalize all the usual resonances, including complex plasmons, real laser resonances in media with gain, and real quasistatic resonances in media with negative permittivity and gain. DOI: 10.1103/PhysRevLett.96.023904 PACS numbers: 41.20.ÿq, 42.25.ÿp It is hard to overestimate the role played by macroscopic electromagnetic resonances in physics. Phenomena and technologies such as lasers, photonic band-gap materials, plasma waves and instabilities, microwave devices, and a great deal of electronics are all related or even entirely based on some kind of electromagnetic resonance. The usual way of analysis consists of deriving the so-called dispersion equation, which relates the wave vector k or the propagation constant jkj of a plane electromagnetic wave to the angular frequency !. The solutions of this equation may be real or complex. In the first case we talk about a real resonance, i.e., such that can be attained for some real angular frequency and therefore, in principle, results in unbounded fields. In reality, however, amplification of the fields is bounded by other physical mechanisms, e.g., nonlinear saturation. If the solution is complex, then we have a complex resonance and, depending on the sign of the imaginary part, the associated fields are either decaying or growing with time. This common approach is rather limited and does not include all pertaining phenomena. Indeed, more or less explicit dispersion equations can be obtained only for infinite (unbounded) homogeneous and periodic media, as often done in plasma and photonic studies. Other approaches impose explicit boundary conditions and can handle resonators and waveguides with perfectly conducting walls, and idealistic piecewise homogeneous objects (e.g., plane layered medium, circular cylinders, a sphere). On the other hand, very little can be said in the general case of a finite inhomogeneous dielectric object situated in free space. Because of the absence of an explicit dispersion equation and explicit boundary conditions, even the existence and classification of resonances in such objects is still an open problem.We describe here an alternative, mathematically rigorous approach to electromagnetic resonances, based on the volume integral formulation of the electromagnetic scattering, also known as the Green's function method and the domain integral equation method. This formulation is equivalent to the Maxwell's equations and is perfectly suited for bounded inhomogeneous objects in free space. Despite its generality, nowadays the volume integral equation is mostly used as a numerical tool, for instance, in near-field optics and geophysics. The main limitation seems to be the implicit ...