Contemporary human life relies heavily on mobile devices such as smart-phone, lap-top, or tablet PC which process tremendous amount of information every day. In near future, rapid development of information technology (IT) would eventually integrate the devices as a wearable and flexible form that will collect and process information ubiquitously. Organic materials and amorphous films have long been studied for the foldable and wearable devices since the devices must be fabricated on a flexible plastic film. However, single-crystalline inorganic semiconductors can provide many advantages over organic materials for optoelectronic and electrical device applications, including high carrier mobility and radiative recombination rates, as well as long-term stability and reliability. Nevertheless, problems associated with high-quality inorganic film growth on flexible substrates represent one of the major obstacles to the use of inorganic semiconductors in flexible and stretchable devices. Previous techniques such as epitaxial growth and lift-off circumvent this problem by separation of the thin film from the growth substrates but difficulty in separating the film from a single-crystal limits their use. Meanwhile, the layered structure of 2-dimentional (2-D) nanomaterials, which consist of weakly bonded layers, makes it easy to transfer the film to foreign substrates. Accordingly, hybrid heterostructures composed of high-quality inorganic thin films or nanostructures grown directly on graphene offer a novel material system for transferable and/or flexible optoelectronics [1,2]. Here I will present controlled growths of ZnO and GaN nano- and micro-structures on 2D nanomaterials using catalyst-free metal-organic vapor phase epitaxy and describe the methods to fabricate flexible LEDs and transistors using the hybrid nanostructures.