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 structures slide on surfaces. I present results of simulations based on Langevin or Brownian-motion dynamics, where the dependence of the linear sliding friction on the temperature and on the coverage is studied. I also present results for the nonlinear (in the external driving force) sliding friction, which is found to exhibit hysteresis giving rise to the well-known phenomenon of ``stick-and-slip'' motion. The theory predicts that for a class of sliding systems the ratio ${\mathit{f}}_{\mathit{k}}$/${\mathit{f}}_{\mathit{s}}$ between the kinetic and the static friction coefficient should equal 1/2, in good agreement with experimental data.