Yet noble metal nanoclusters and other nanoparticles are nowadays extensively studied at experimental level for fostering numerous applications such as high-performance colorimetric sensing, heterogeneous catalysis or surface-plasmon-assisted catalysis, just to cite some of them. This enthusiasm for noble metal nanostructures is in part related to their localized surface plasmon resonance (LSPR) activity and its induced properties. The collective and coherent oscillations of their conduction electrons (plasmons) in response to an external electromagnetic field lead to impressive optical properties. Well tuned in terms of size, shape and surrounding environment, noble metal nanostructures exhibit a strong and enhanced absorption band in the UV/vis/NIR region. In time, pioneering investigations devoted to LSPR of large nanoparticles (e.g., 50 to 100 nm) have been extended to much smaller systems. This increasing interest is concomitant to the recent success in synthesizing highly stable small nanostructures, and the willing to address the miniaturization issue in plasmonics. Beyond a size limit of about 10 nm, the plasmon excitations in noble metal nanoparticles are typically considered as a continuum. They are well described by more or less sophisticated classical electrodynamics models. Below this threshold, the continuum description starts to fail due to the strong size dependence of the dielectric constant. An accurate description of the plasmon excitations is based on empirically-tuned dielectric constants or nonlocal dielectric models. The failure becomes even more dramatic when the size of the noble metal nanoparticle reaches 2 nm. For this range of size, the system is commonly considered as a nanocluster rather than a nanoparticle. It becomes 'finite' and behaves as a molecule.