The wide variety of applications of metal nanoparticles has motivated many studies of their properties. Some important practical issues are how the size, composition and structure of these materials affect their catalytic and optical properties. In this article we review our recent work on the photophysics of metal nanoparticles. The systems that have been investigated include Au particles with sizes ranging from 2 nm diameter (several hundred atoms) to 120 nm diameter, and bimetallic core-shell particles composed of Au, Ag, Pt and/or Pb. These particles, which have a rather narrow size distribution, are prepared by radiolytic techniques. By performing time-resolved laser measurements we have been able to investigate the coupling between the electrons and phonons in the particles, and their low frequency "breathing" modes. These experiments show that for Au the time scale for electron-phonon coupling does not depend on size, in contrast to metals such as Ga and Ag. On the other hand, the frequency of the acoustic breathing modes strongly depends on the size of the particles, as well as their composition. These modes are impulsively excited by the rapid lattice heating that accompanies ultrafast laser excitation. The subsequent coherent nuclear motion modulates the transmitted probe laser intensity, giving a "beat" signal in our experiments. Unlike quantum-beats in molecules or semiconductors, this signal can be completely understood by classical mechanics.