Flutter is a self-excited vibration under the interaction of the inertial force, aerodynamic force, and elastic force of the structure. After the flutter occurs, the aircraft structures will exhibit limit cycle oscillation, which will cause catastrophic accidents or fatigue damage to the structures. Therefore, it is of great theoretical and practical significance to study the aeroelastic characteristics and flutter control for improving the aeroelastic stability of aircraft structures. This paper reviews the recent advances in aeroelastic analysis and flutter control of wings and panel structures. The mechanism of aeroelastic flutter of wings and panels is presented. The research methods of aeroelastic flutter for different structures developed in recent years are briefly summarized. Various control strategies including the linear and nonlinear control algorithms as well as the active flutter control results of wings and panels are presented. Finally, the paper ends with conclusions, which highlight challenges of the development in aeroelastic analysis and flutter control, and provide a brief outlook on the future investigations. This study aims to present a comprehensive understanding of aeroelastic analysis and flutter control. It can also provide guidance on the design of new wings and panel structures for improving their aeroelastic stability.