On the basis of a kinetic growth model we discuss new methods to grow atomically flat homoepitaxial layers in a controlled way. The underlying principle of these methods is to change the growth parameters during growth of an atomic layer in such a way that nucleation on top of a growing layer is suppressed, and thus, layer-by-layer growth is achieved. Experimentally, this can be realized by changing the substrate temperature or deposition rate during monolayer growth in a well-defined way. The same can be achieved at constant temperature and deposition rate by simultaneous ion bombardment during the early stages of growth of a monolayer, or by adding suitable surfactants to the system. Model experiments on Ag(lll) and on Cu(lll) using thermal energy atom scattering and scanning tunneling microscopy demonstrate the success of these methods.