We study static and dynamic properties of polymer brushes of moderate and high grafting densities using molecular dynamics simulations. The self-consistent-field theory is able to reproduce the observed density profiles once finite extensibility of the chains is included. A similar approach, using a Langevin-type model to account for a coupling between the vertical and lateral chain fluctuations, is successfully implemented to explain the lateral chain fluctuations at moderate-to-high grafting densities. The corresponding fluctuation dynamics in the direction lateral to the surface is well described by Rouse scaling. The dependence of the dynamics on grafting density (concentration) is very well described by the dynamic behavior of thermal blobs for the fluctuations in the direction both perpendicular and parallel to the surface. We find an anisotropic fluctuation dynamics related with two characteristic dynamic length scales in the both directions. We have further investigated the pulling forces acting on the polymer bonds. The force acting on the first bond directly connected to the surface is reduced at higher grafting densities, which is explained with an entropic contribution to the bond tension. A nonvanishing end-monomer tension is observed at high grafting densities. The integrated force (excess free energy) follows the prediction of the thermal blob model of the brush.