Graphene sheets having a plurality of holes in their basal planes are described herein. Methods for making the graphene sheets can involve contacting graphene sheets with an activated gas that has contacted a helium or argon atmospheric pressure plasma. The size and/or number of holes introduced can be altered by changing the contact time, the stand-off distance, the activated gas concentration, and/or the plasma power. Polymer composites containing the perforated graphene sheets are also described.