The atomistic processes that form the basis of thin film growth often involve complex multi-atom movements of atoms or groups of atoms on or close to the surface of a substrate. These transitions and their pathways are often difficult to predict in advance. By using an adaptive kinetic Monte Carlo (AKMC) approach many complex mechanisms can be identified so that the growth processes can be understood and ultimately controlled. Here the AKMC technique is briefly described along with some special adaptions that can speed up the simulations when, for example, the transition barriers are small. Examples are given of such complex processes that occur in different material systems especially for the growth of metals and metallic oxides.