Stimuli-responsive polymer materials can change their structure and physical properties drastically on external signals like a change in temperature, solvent properties (pH, ionic strength), the magnetic or electrical field etc. Such "smart" polymer materials play an important role in various fields such as biology, medicine, and soft materials. However, it is a great challenge to investigate such "smart" polymer materials due to highly inhomogeneous structure at the molecular scale and the complex interactions. In this thesis, we have systematically studied three common types of stimuli-responsive polymer brushes such as temperature responsive polymer brushes, copolymer brushes, and mixed polymer brushes by using classical density functional theory. We find a surface outer layer switch for both copolymer brushes and mixed polymer brushes with a selective solvent. Without using any temperature-dependent parameter, our theory successfully captures the lower critical solution temperature behavior of the associating polymer brushes. Related parameters such as molecular weight, grafting density, and solvent properties that affect the phase behavior of these stimuli-responsive polymer brushes have been also investigated. Qualitatively consistent with experimental observations, our results provide physical insight and helpful guidance for the experimental design of such stimuli-responsive polymer materials.