When an external force acts on an adsorbate structure, the structure may slide or flow relative to the substrate. The mechanism behind this sliding motion is of fundamental importance for the understanding of friction and lubrication between two flat macroscopic surfaces, and is also related to the question of what boundary condition should be used for the velocity field at a solid-liquid interface when solving the Navier-Stokes equations of fluid dynamics. Here I study the friction which occurs when adsorbate layers slides on surfaces. I present results of simulations based on Langevin or Brownian-motion dynamics, which illustrate the dependence of the nonlinear (in the external driving force Fl sliding friction eta on the coverage theta,and on the microscopic friction eta. The sliding friction (as a function of Fl exhibit three dynamical phase transitions, namely (commensurate solid-->incommensurate solid), (fluid-->incommensurate solid) and (fluid-->incommensurate solid) transitions. The role of static imperfections (pinning centers) on the sliding dynamics is also discussed.