Graphene has been attracting wide attention owing to its superb electronic, thermal and mechanical properties. These properties allow great applications in the next generation of optoelectronics, where flexibility and stretchability are essential. In this context, the recent development of graphene growth/transfer and its applications in field-effect transistors are involved. In particular, we provide a detailed review on the state-of-the-art of graphene-based flexible and stretchable thin film transistors. We address the principles of fabricating high-speed graphene analog transistors and the key issues of producing an array of graphene-based transistors on flexible and stretchable substrates. It provides a platform for future work to focus on understanding and realizing high-performance graphene-based transistors.