The surface plasmon resonance (SPR) of noble metal nanoparticles is reviewed in terms of both classical and quantum mechanical approaches. The collective oscillation of the free electrons responsible for the plasmon is well described using classical electromagnetic theory for large systems (from about 10 to 100 nm). In cases where quantum effects are important, this theory fails and first principle approaches like time-dependent density functional theory (TDDFT) must be used. In this paper, we give an account of the current understanding of the quantum mechanical origin of plasmon resonances. We provide some insight into how the discrete absorption spectrum of small noble metal clusters evolves into a strong plasmon peak with increasing particle size. The collective character of the plasmon is described in terms of the constructive addition of single-particle excitations. As the system size increases, the number of single-particle excitations increases as well. A configuration interaction (CI) approach can be applied to describe the optical properties of particles of all shapes and sizes, providing a consistent definition of plasmon resonances. Finally, we expand our analysis to thiolate-protected nanoparticles and analyze the effects of ligands on the plasmon.