## 1 Introduction
The electrical size is expressed through the size parameter defined as \(x=\omega\sqrt{\varepsilon_{\text{host}}\varepsilon_{0}\mu_{\text{host}}\mu_ {0}}r_{1}=\frac{2\pi}{\lambda}r_{1}\), where \(\omega\sqrt{\varepsilon_{\text{host}}\varepsilon_{0}\mu_{\text{host}}\mu_ {0}}=k\) is the wavenumber of the host medium. The first, mathematically rigorous attempts explaining the triggered mechanisms, therefore quantifying the scattering behavior, were derived by [PERSON] for the case of a very small scatterer (electrostatic case) [45; 46; 47]. Almost simultaneously, developments attributed to workers such as [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] gave birth to a more complete electrodynamic perspective about this problem, always in accordance with the [PERSON] equations [18; 48]. In both aforementioned cases, the mathematical treatment of the problem is similar: assuming a plane wave excitation and requiring that both outside and inside regions [PERSON]'s equations are satisfied, one can derive a set of electrical and magnetic field expressions, expanded in the spherical coordinate system [16; 49]. These expressions contain a set of unknown amplitude coefficients, the Mie coefficients [19]. The determination of these coefficients requires the solution of the formulated boundary value problem, i.e., the continuity of all tangential field components at the interface (or interfaces if we have multilayered sphere), assuming that the acceptable solutions consist of properly behaving functions that vanish at infinity and are well behaved in the origin of the sphere. A complete and systematic analysis for this problem can be found in several text-books [16; 18; 19]. Here, we will try to unravel the resonant features of the Mie coefficients and analyze their physical implications. Section 2 conveys a brief discussion on the full-electrodynamic scattering perspective, the Mie coefficients, where the spectrum of a homogeneous dielectric sphere as a function of the permittivity and the size parameter is given. The study of the scattering spectrum reveals the existence of two different resonant features, the localized surface plasmon (LSPR or plasmonic) and the dielectric resonances, respectively. Plasmonic resonances (LSPRs are generally different from their surface and volume counterparts, since LSPRs are non-propagating resonances, directly triggered by the impinging radiation [50]) occur from the coupling between the free electrons (plasma, \(\varepsilon<0\)) in metals with the electromagnetic field [50, 51]. This collective effect involves both the electric and kinetic energy of the free electrons, hence is of primarily electric character and can be observed even for deeply subwavelength structures [52]. However, the second type of resonances, i.e., the dielectric resonances, are of either magnetic or electric character, highly dependent on the dielectric contrast of the sphere. The dielectric resonances exhibit a more complicated field distribution inside the scatterer. These resonances are also called morphology-dependent resonances (MDR) [53], or Mie resonances [4] occurring for \(\varepsilon>0\). In Section 3, a brief description of the electrostatic (Rayleigh) problem is given, exposing the nature of the plasmonic resonances on a subwavelength sphere. A connection between the Rayleigh picture and the plasmon hybridization is briefly discussed for the case of a resonant core-shell sphere. Section 4 begins with a revision of the Mie-Taylor approximation, an alternative way to reach the Rayleigh picture, offering a clear connection between the electrostatic and the Mie theory perspective. A more complete picture encompassing the resonant features of the Mie coefficients, i.e., size-induced dynamic characteristics, is obtained by the Mie-Pade approximation. Valuable information regarding these scattering processes are extracted, and generalized resonant formulae of the resonant magnetic and electric multipoles are exposed in Section 5.