The scattering problem by immersed targets involves the resonance phenomenon. Different methods of isolation of modal resonances are discussed: the Resonant Scattering Theory (the different backgrounds used in this method are considered), the phase gradient method (which is partly independent of the background choice), and the Argand diagram method (leading to both theoretical and experimental determination of the frequency and the width of resonances) and an exact description of the resonance components of partial modes (involving the determination of the roots of the characteristic equation in the complex frequency plane). The results provided by these methods are compared, their validity domain is discussed. Whatever the method, the resonant components appear as Breit-Wigner functions: this is the common point between the different methods. This review article includes 119 references.

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