Abstract: When common polymers and graphene are incorporated into one composite, some parts of properties of graphene materials are often degraded, such as high electrical and thermal conductivities, or high specific surface area, etc, which leads to much application restriction of graphene/polymer composites. If some specific applications are targeted, through designing or choosing corresponding functional polymers, the needed properties of graphene/polymer composites can be specifically enhanced and the performance can be improved, so that the application restriction of graphene/polymer composites will be weakened or eliminated. In this review, based on the definition of functional polymers above, the recent advancements on the preparation and applications of graphene/functional polymer composites are summarized according to dimensions of graphene material parts. The remained challenges in this field are also discussed.