Polymer chains anchored with one end at a hard wall are investigated by Monte Carlo simulations using the bond-fluctuation model. We present results for several different interesting situations: (1) grafted layers in the good and poorer solvent conditions, (2) grafted layers under the effect of shear solvent flow, (3) the formation/desorption kinetics of the grafted layers, and (4) the behavior of a layer of binary mixture of incompatible grafted chains.