Atom-embedding calculations and Monte Carlo simulations are presented on various topics which are important for a better understanding of homoepitaxial growth of metals. Results of realistic simulations of the homoepitaxial growth on Cu(100) are presented for the submonolayer regime as well as for multilayer growth. Where possible, the results are compared with existing theories, and available experimental data. A good overall agreement is observed. Atom-embedding calculations are used to investigate the role of surfactants to stimulate smoother growth of metal surfaces. The atomic processes which may be responsible for a successful surfactant action are illustrated by atom-embedding calculations for the homoepitaxial growth on Cu(100) and Cu(111) with In as a surfactant.