Surface plasmon excitation in metal nanoparticles has found great interest in the past. This collective oscillation of the conduction electrons can be stimulated with light and is characterized by resonances, whose positions depend on the material, the dimensions and the dielectric surrounding of the particles. Recently, the investigation of the ultrafast dephasing time T2 and of the decay mechanisms of surface plasmon excitation have become of particular importance, an essential reason being that T2 is proportional to the enhancement factor of the electric field in the vicinity of the nanoparticle surface. This enhancement plays a key role in a great variety of applications. The present paper presents an overview of our recent experiments on the ultrafast decay of surface plasmon excitation, in particular by using a technique that allows us to measure the homogeneous line widths of surface plasmon resonances in the presence of inhomogeneous broadening and thus determine T2. The method is based on persistent spectral hole burning in the absorption profiles of supported metal nanoparticles by nanosecond laser pulses. The technique has been systematically applied to silver and, more recently, to gold nanoparticles on different substrates. Size and shape dependent dephasing times ranging from 2.6 to 15 fs have been extracted from the experimental results using a theoretical model. The values reflect the reduced dimensions of the nanoparticles and we conclude that additional damping mechanisms, in particular surface scattering and chemical interface damping, come into play.