This dissertation discusses several closely related problems involving end attached polymers at interfaces. The studies share a numerical self-consistent field approach which is described in detail in Chapter 1. In Chapter 2, we consider irreversible polymer brushes (polymers densely end tethered to a surface). First, we discuss the adequacy of second virial treatments of interchain interactions. Next we examine the extent of interbrush penetration between compressed polymer brushes, and its effect on the interactions between them. Then we identify scaling variables which control the behavior of polymer brushes in polymeric solvents. Finally we investigate brush configurations and interactions in mixed solvents, where nonmonotonic interaction profiles are predicted with a longer range weak attraction, and strong repulsion at shorter separations. In Chapter 3, we discuss the modification of spreading properties of a liquid on a solid surface by the addition of end-adsorbing polymers. An end-adsorption polymer additive can lead an otherwise non-spreading liquid to spread. A phase diagram for spreading of a liquid drop of fixed volume as a function of the concentration of end-adsorbing polymers and the energy of end-adsorption to the surface is obtained. The equilibrium thickness of a spread film is also calculated, and is shown to be closely related to the thickness of a self-assembled polymer brush in an unbounded fluid and relatively insensitive to the bare spreading power of the liquid or the Hamaker constant, which determine the equilibrium thickness of a film of a simple liquid. Finally, in Chapter 4, we study the interaction forces between two plates in a semi-dilute solution of polymers each having one weakly adsorbing end-group. This system exhibits both repulsive and attractive interactions of comparable magnitude and well-separated length scales. The repulsion has a length scale of the end-to-end distance of the endadsorbed polymer, and a magnitude which is proportional to the end-adsorption energy and the volume fraction of the polymer, and inversely proportional the chain molecular weight. At plate separations of order the correlation length of the solution, a depletion attraction sets in with a magnitude that scales with the bulk osmotic pressure.