The ability to manufacture tailored graphene nanostructures is a key factor to fully exploit its enormous technological potential. We have investigated nanostructures created in graphene by swift heavy ion induced folding. For our experiments, single layers of graphene exfoliated on various substrates and freestanding graphene have been irradiated and analyzed by atomic force and high resolution transmission electron microscopy as well as Raman spectroscopy. We show that the dense electronic excitation in the wake of the traversing ion yields characteristic nanostructures each of which may be fabricated by choosing the proper irradiation conditions. These nanostructures include unique morphologies such as closed bilayer edges with a given chirality or nanopores within supported as well as freestanding graphene. The length and orientation of the nanopore, and thus of the associated closed bilayer edge, may be simply controlled by the direction of the incoming ion beam. In freestanding graphene, swift heavy ion irradiation induces extremely small openings, offering the possibility to perforate graphene membranes in a controlled way.