Graphene, a single atomic layer of graphite, has been the focus of recent intensive studies due to its novel electronic and structural properties. Metals grown on graphene also have been of interest because of their potential use as metal contacts in graphene devices, for spintronics applications, and for catalysis. All of these applications require good understanding and control of the metal growth morphology, which in part reflects the strength of the metal–graphene bond. Also of importance is whether the interaction between graphene and metal is sufficiently strong to modify the electronic structure of graphene. In this review, we will discuss recent experimental and computational studies related to deposition of metals on graphene supported on various substrates (SiC, SiO2, and hexagonal close-packed metal surfaces). Of specific interest are the metal–graphene interactions (adsorption energies and diffusion barriers of metal adatoms), and the crystal structures and thermal stability of the metal nanoclusters.