Using atomistic computer simulations, we study how ion irradiation can be used to alter the morphology of a graphene monolayer by introducing defects of specific type, and to cut graphene sheets. Based on the results of our analytical potential molecular dynamics simulations, a kinetic Monte Carlo code is developed for modelling morphological changes in a graphene monolayer under irradiation at macroscopic time scales. Impacts of He, Ne, Ar, Kr, Xe and Ga ions with kinetic energies ranging from tens of eV to 10 MeV and angles of incidence between 0\circ and 88\circ are studied. Our results provide microscopic insights into the response of graphene to ion irradiation and can directly be used for the optimization of graphene cutting and patterning with focused ion beams.
