Microelectromechanical systems (MEMS) that are based on flexible substrates are widely used in flexible, reconfigurable radio frequency (RF) systems, such as RF MEMS switches, phase shifters, reconfigurable antennas, phased array antennas and resonators, etc. When attempting to accommodate flexible deformation with the movable structures of MEMS, flexible RF MEMS are far more difficult to structurally design and fabricate than rigid MEMS devices or other types of flexible electronics. In this review, we survey flexible RF MEMS with different functions, their flexible film materials and their fabrication process technologies. In addition, a fabrication process for reconfigurable three-dimensional (3D) RF devices based on mechanically guided assembly is introduced. The review is very helpful to understand the overall advances in flexible RF MEMS, and serves the purpose of providing a reference source for innovative researchers working in this field.