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