The cross-medium aircraft is a new type of aircraft that can sail in the air and under the water. The water-entry process of the cross-medium aircraft plays a vital role in its performance. This paper begins with an overview of the water-entry problem of a cross-medium aircraft. The research status and development trends of cross-medium aircraft crossing different mediums at home and abroad are introduced in detail. The dynamic model and trajectory optimization problems are studied for the water-entry process of the cross-medium aircraft. Firstly, the shape of the cross-medium aircraft is introduced. Then the force analysis of the water-entry process is carried out, and the dynamic model of the water-entry process is established. Based on the established dynamic model, the water-entry process is treated as a free motion to avoid instability caused by switching complex control strategies. Therefore, the water-entry trajectory of the cross-medium aircraft is determined by the state of motion before reaching the water. To optimize the water-entry trajectory under different mission requirements, particle swarm optimization algorithm is applied, and the water-entry speed, water-entry angle and angle of attack are regarded as the optimization variables. Simulation experiments are conducted to verify the rationality of the dynamical model and the effectiveness of the proposed trajectory optimization algorithm. The results demonstrate that the change law of the water-entry trajectory and the control variables that meets the task requirements is obtained.