We consider the role of deformations in graphene heterostructures with hexagonal crystals (including strain, wrinkles and dislocations) on the geometrical properties of moiré patterns characteristic for a pair of two incommensurate misaligned isostructural crystals. By employing a phenomenological theory to describe generic moiré perturbations in van der Waals heterostructures of graphene and hexagonal crystals we investigate the electronic properties of such heterostructures.