With the rapid development of unmanned systems technology, their applications in high-precision, high-risk, and complex environment missions are becoming more and more widespread. However, unmanned systems face many optimization challenges in practical applications, such as trajectory planning and tracking, formation control, decision-making and task allocation, and control optimization. Traditional optimization methods are often inadequate in dealing with these complex problems. In this paper, based on the current state of unmanned systems optimization, several types of neurodynamic optimization methods are introduced, and their unique advantages in unmanned systems optimization are discussed. Then, the mathematical characteristics and difficulties of several types of key optimization problems in unmanned systems are analyzed in detail, and the specific applications and effectiveness of neurodynamic optimization methods in these problems are summarised. Finally, the paper looks forward to the future development direction of neurodynamic optimization in the field of unmanned systems and emphasizes its important role in improving the performance, safety, and intelligence of unmanned systems.