The increasing demand for multifunctional polymer nanocomposites calls for new technologies to simultaneously enhance mechanical, electrical, and thermal properties. This paper presents the use of an alternating-current electric field to align graphene nanoplatelets (GnPs) in an epoxy polymer. Theoretical modeling of the alignment process has identified the key parameters that control the rotation and chain-formation of the GnPs. Experimental results reveal that the resulting nanocomposites exhibit anisotropic properties with significantly improved electrical and thermal conductivities in the alignment direction, and dramatically increased fracture toughness when the GnPs are aligned transverse to the crack growth direction. In particular, compared to the unmodified epoxy polymer, the alignment of the GnPs yields up to about 7-8 orders of magnitude improvement in the electrical conductivity, up to approximately 60% increase in the thermal conductivity, and up to a nearly 900% increase in the mode I fracture toughness. The dramatic improvement in the fracture toughness is attributed to multiple intrinsic and extrinsic toughening mechanisms including microcracking, pinning, deflection and branching of the crack, and rupture and pull-out of the GnPs. Such major improvement in the toughness arises from GnPs being transversely aligned to the crack growth direction exhibiting increased interactions with the advancing crack tip.