This paper presents a comprehensive analysis of simple models useful to analyze the growth of nanostructures obtained by cluster deposition. After detailing the potential interest of nanostructures, I extensively study the first stages of growth (the submonolayer regime) by kinetic MonteCarlo simulations. These simulations are performed in a wide variety of experimental situations : complete condensation, growth with reevaporation, nucleation on defects, total or null clustercluster coalescence . . . . The main scope of the paper is to help experimentalists analyzing their data to deduce which of those processes are important and to quantify them. A software including all these simulation programs is available at no cost on request to the author. I carefully discuss experiments of growth from cluster beams and show how the mobility of the clusters on the surface can be measured : surprisingly high values are found. An important issue for future technological applications of cluster deposition is the relation between the size of the incident clusters and the size of the islands obtained on the substrate. An approximate formula which gives the ratio of the two sizes as a function of the melting temperature of the material deposited is given. Finally, I study the atomic mechanisms which can explain the diffusion of the clusters on a substrate and the result of their mutual interaction (simple juxtaposition, partial or total coalescence . . . ).