Forming nanostructures on the solids surface is one of the promising nanotechnological processes. It has been established that changes in the atomic structure of the solid surface due to the formation of nanostructures result both in a significant change in various physical properties of the surface, and in an increase in its durability, strength, hardness, wear resistance and defects on the surface healing. There are many different methods for forming nanostructures on solid surfaces: surface modification with nano-elements (nanoparticles, fullerenes and fullerites, graphene and nanotubes), formation of a nanocomposite layer on the surface, forming quantum dots and whiskers on the surface, implantation of ions into the solid surface, laser surface treatment and other processes. The above processes are very complex and for their optimization require detailed research both by experimental and theoretical methods of mathematical modeling [1-2]. The paper provides a comparative review of different methods of forming nanostructures on the solids surface and various aspects of mathematical modeling of these processes.