Owing to their extraordinary electrical, chemical, optical, mechanical and structural properties, graphene and its derivatives have stimulated exploding interests in their sensor applications ever since the first isolation of free-standing graphene sheets in year 2004. This article critically and comprehensively reviews the emerging graphene-based electrochemical sensors, electronic sensors, optical sensors, and nanopore sensors for biological or chemical detection. We emphasize on the underlying detection (or signal transduction) mechanisms, the unique roles and advantages of the used graphene materials. Properties and preparations of different graphene materials, their functionalizations are also comparatively discussed in view of sensor development. Finally, the perspective and current challenges of graphene sensors are outlined (312 references).