Three-dimensional graphene nanosheets (3D-GNS) were used as cathode catalysts for microbial fuel cells (MFCs) operating in neutral conditions. 3D-GNS catalysts showed high performance towards oxygen electroreduction in neutral media with high current densities and low hydrogen peroxide generation compared to activated carbon (AC). 3D-GNS was incorporated into air-breathing cathodes based on AC with three different loadings (2, 6 and 10 mgcm(-2)). Performances in MFCs showed that 3D-GNS had the highest performances with power densities of 2.059 +/- 0.003 Wm(-2), 1.855 +/- 0.007 Wm(-2) and 1.503 +/- 0.005 Wm(-2) for loading of 10, 6 and 2 mgcm(-2) respectively. Plain AC had the lowest performances (1.017 +/- 0.009 Wm(-2)). The different cathodes were also investigated in supercapacitive MFCs (SC-MFCs). The addition of 3D-GNS decreased the ohmic losses by 14-25%. The decrease in ohmic losses allowed the SC-MFC with 3D-GNS (loading 10 mgcm-2) to have the maximum power (P-max) of 5.746 +/- 0.186 Wm(-2). At 5 mA, the SC-MFC featured an "apparent" capacitive response that increased from 0.027 +/- 0.007 F with AC to 0.213 +/- 0.026 F with 3D-GNS (loading 2 mgcm(-2)) and further to 1.817 +/- 0.040 F with 3D-GNS (loading 10 mgcm(-2)). (C) 2017 The Authors. Published by Elsevier B.V.