Despite the widespread interest in graphene electronics over the past decade, high-performance graphene field-effect transistors (GFETs) on flexible substrates have been rarely achieved, even though this atomic sheet is widely understood to have greater prospects for flexible electronic systems. In this article, we report detailed studies on the electrical and mechanical properties of vapor synthesized high-quality monolayer graphene integrated onto flexible polyimide substrates. Flexible graphene transistors with high-k dielectric afforded intrinsic gain, maximum carrier mobilities of 3900 cm(2)/V·s, and importantly, 25 GHz cutoff frequency, which is more than a factor of 2.5 times higher than prior results. Mechanical studies reveal robust transistor performance under repeated bending, down to 0.7 mm bending radius, whose tensile strain is a factor of 2-5 times higher than in prior studies. In addition, integration of functional coatings such as highly hydrophobic fluoropolymers combined with the self-passivation properties of the polyimide substrate provides water-resistant protection without compromising flexibility, which is an important advancement for the realization of future robust flexible systems based on graphene.