Heterostructures prepared from graphene and fluorographene (FG) using the technology of 2D printing on solid and flexible substrates were fabricated and studied. Excellent stability of printed graphene layers and, to a lesser degree, composite graphene:PEDOT:PSS layers were shown. Extraordinary properties of FG as an insulating layer for graphene-based heterostructures at fluorination degree above 30% were demonstrated. It is shown that the leakage current in thin (20-40 nm) films is normally smaller than 10 -8 A/cm 2 , the breakdown field being greater than 10 8 V/cm. In hybrid structures with printed FG layers in which graphene was transferred onto, or capsulated with, an FG layer, an increase in charge-carrier mobility and material conductivity amounting to 5-6 times was observed. The spectrum of future applications of FG layers can be further extended due to the possibility of obtaining, from weakly fluorinated graphene (<20%), functional layers exhibiting a negative differential resistance behavior and, at fluorination degrees of 20-23%, field-effect-transistor channels with current modulation reaching several orders. Composite or bilayer films based on fluorographene and V 2 O 5 or polyvinyl alcohol exhibit a stable resistive switching behavior. On the whole, graphene/FG heterostructures enjoy huge potential for their use in a wide spectrum of application, including flexible electronics.