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The scattering of electromagnetic waves by resonant systems is determined bythe excitation of quasinormal modes (QNMs), i.e., the eigenmodes of the system.This Review addresses three fundamental concepts in relation with therepresentation of the scattered field as a superposition of the excited QNMs:normalization, orthogonality, and completeness. Orthogonality and normalizationenable a straightforward assessment of the QNM excitation strength for anyincident wave. Completeness guaranties that the scattered field can befaithfully expanded into the QNM basis. These concepts are non-trivial fornon-conservative (non-Hermitian) systems and have driven many theoreticaldevelopments since initial studies in the 70's. Yet, owing to recentachievements, they are not easily grasped from the extensive and scatteredliterature, especially for newcomers in the field. After recalling fundamentalresults obtained in early studies on the completeness of the QNM basis forsimple resonant systems, we review recent achievements and debates on thenormalization, clarify under which circumstances the QNM basis is complete, andhighlight the concept of QNM regularization with complex coordinate transform.

Normalization, orthogonality and completeness of quasinormal modes of open systems: the case of electromagnetism