The research on advanced functional polymers is being driven by the fast-growing demand for new functional materials that can be used in revolutionary technologies. Polymers can be endowed with functions by using certain special preparation methods or by introducing functional groups or fillers into materials. These functions are either intrinsically possessed by materials or actuated by external stimuli. In this review, we present an overview of the recent developments made in the research hotspots of functional polymers, encompassing polymerization methodologies, luminescent polymers, photovoltaic polymers, other electronic and optical polymers (including low-k polyimides and second-order nonlinear optical polymers), biorelated polymers (particularly those for biomedical applications), supramolecular polymers, stimuli-responsive polymers, shape-memory polymers, separation polymer membranes, energy storage polymers, and covalent organic framework polymers. The concepts, design strategies at the molecular level, preparation methods, classifications, properties, potential applications, and recent progress made in such polymers are summarized. Challenges and future perspectives of each type of functional polymers are also addressed, including research efforts regarding the design and fabrication of functional polymers for serving the increasing demand for new materials.