Interfacial mechanics between graphene and substrate such as adhesion and friction plays a critical role in the morphology and functionality of graphene-based devices. Here I will present our recent work on adhesion and interfacial shear stress transfer of graphene. In the first part, I will present a new method that can measure adhesion energies between ultraflat graphene and a broad range of materials using atomic force microscopy (AFM) with a microsphere tip. In our experiments, only van der Waals force between the tip and a graphene flake is measured. The Maugis-Dugdale theory is employed to calculate the adhesion energy. The ultraflatness of monolayer graphene on mica eliminates the effect of graphene surface roughness on the adhesion, while roughness of the microsphere tip is addressed by the modified Rumpf model. Adhesion energies of monolayer graphene to SiO2 and Cu are obtained as 0.46 and 0.75 Jm-2, respectively. In the second part, I will present the nonlinear mechanical response of monolayer graphene on polyethylene terephthalate (PET), which is characterised using in-situ Raman spectroscopy and AFM. While interfacial stress transfer leads to tension in graphene as the PET substrate is stretched, retraction of the substrate during unloading imposes compression in the graphene. Two interfacial failure mechanisms, shear sliding under tension and buckling under compression, are identified. Using a nonlinear shear-lag model, the interfacial shear strength is found to range between 0.46 and 0.69 MPa. The critical strain for onset of interfacial sliding is ∼ 0.3%, while the maximum strain that can be transferred to graphene ranges from 1.2% to 1.6% depending on the interfacial shear strength and graphene size. Beyond a critical compressive strain of around −0.7%, buckling ridges are observed after unloading. I will end the presentation with tuning the morphology and multifunctionality of monolayer 2D nanomaterials using mechanical strain.