Graphene-based nanocomposites are largely explored for the development of sensing devices due to the excellent electrical and mechanical properties of graphene. These properties, in addition to its large specific surface area, make graphene attractive for a wide range of chemical functionalization and immobilization of (bio)molecules. Several techniques based on both top-down and bottom-up approaches are available for the fabrication of graphene fillers in pristine and functionalized forms. These fillers can be further modified to enhance their integration with polymeric matrices and substrates and to tailor the sensing efficiency of the overall nanocomposite material. In this review article, we summarize recent trends in the design and fabrication of graphene/polymer nanocomposites (GPNs) with sensing properties that can be successfully applied in environmental and human health monitoring. Functional GPNs with sensing ability towards gas molecules, humidity, and ultraviolet radiation can be generated using graphene nanosheets decorated with metallic or metal oxide nanoparticles. These nanocomposites were shown to be effective in the detection of ammonia, benzene/toluene gases, and water vapor in the environment. In addition, biological analytes with broad implications for human health, such as nucleic bases or viral genes, can also be detected using sensitive, graphene-based polymer nanocomposites. Here, the role of the biomolecules that are immobilized on the graphene nanomaterial as target for sensing is reviewed.