Sophisticated DFT analysis show that presence of solvent molecules gives rise to swelling of polymer brushes. This effect is very interesting in the context of studying the effect of quality of solvent on the brushes. Also, numerical solution of the DFT equations shows that when a polymer star as a typical macromolecular inclusion interpenetrates into a brush, simultaneously it squeezes. The equation of state of a polymer star proven to be scaled as N -2/5 , it means that by increasing the degree of polymerization, the outward pressure inside the polymer star decreases. Polymer brush bilayers are also investigated here by means of the DFT, the scaling theory and the molecular dynamic simulations (MD). It turns out that the equation of state a brush bilayer scales as (N/D) which means that the pressure is very strongly dependent on the degree of polymerization as well as the walls distance. Polymer brush bilayers under stationary shear show two distinct scenarios based on the strength of shear rate. A low shear rate appears when the brushes are sheared but they still interpenetrate. In the absence of the hydrodynamic interactions in the low shear rate scenario, the shear stress scales as W 3/2 . However, when we switch on the hydrodynamic interactions in the low shear scenario, the shear stress scales as W 0.8 . As the shear rate increases more, the chain stretch strongly in the shear direction and the interpenetration disappears. This is the high shear rate scenario. In the high shear rate scenario, in the absence of the hydrodynamic interactions, the shear stress scales as W . However, when we switch on the hydrodynamic interactions in this scenario, it turns out that the shear stress scales as W 2/3 . Note that the universal power law W 2/3 has been already predicted by a method so called blob picture. Therefore, we can conclude that this is the hydrodynamic interactions between monomers that is responsible for the shear thinning effect in polymer brush bilayers. Without hydrodynamic interactions there is no sublinear regime. In most biological systems that polymer brush bilayers reside, the system is in non-equilibrium conditions. The most familiar situation is the shear inversion motion in the synovial joints of mammals. The MD simulations show that at a certain moment after inversion takes place, the shear stress increases. It turns out that the hydrodynamic interactions between monomers leads a very sharp overshoot in moment of high shear stress. However, when we switch on the electrostatic interactions between monomers, the overshoot of the shear stress is suppressed. This suggests that presence of charged monomers in brush bilayers, decrease mechanical instabilities which are the source of Musculoskeletal diseases in joints. And finally, we saw that by means a powerful mathematical method like the DFT and numerical technique like the MD, we can approach the very complicated soft matter and biological systems such as polymer brushes. This article paves the way for more researches in order to get more knowledge about these systems.