Functional two-dimensional nanomaterials are emerging in a variety of applications, for instance ascatalysts for chemical reactions, as substrates that direct and align adsorbed molecules and as insulating layers to decouple adsorbates from the metal. We investigate adsorption, assembly, dynamics, and reactions at metallic and oxide surfaces, focusing on the atomic scale understanding of physical properties at interfaces, such as interactions between adsorbate and underlying surface, lateral interactions between adsorbates, nanoscale friction, and local effects of the environment dynamics. The fundamental insight into these aspects is required for the control of processes. Among other analysis tools, we also extend and apply methods to reproduce STM and AFM images by simulations based on electronic structure calculations at the DFT level of theory. Our theoretical studies provide important details on the structure, properties, and functionality of the selected two-dimensional materials, highlighting the importance of simulations for the interpretation of experimental results and for the modeling and prediction of properties.