We show that graphene nano-sheets, when appropriately functionalised, can form self-assembling nanocontainers which may be opened or closed using a chemical trigger such as pH or polarity of solvent. Conceptual design rules are presented for different container structures, whose ability to form and encapsulate guest molecules is verified by molecular dynamics simulations. The structural simplicity of the graphene nanocontainers offers considerable scope for scaling the capacity, modulating the nature of the internal environment, and defining the trigger for encapsulation or release of the guest molecule(s). This design study will serve to provide additional impetus to developing synthetic approaches for selective functionalisation of graphene.