Motion or trajectory planning is a key aspect of the advances in the performance and autonomy of spacecraft operations. However, the computational resources of spacecraft are still limited. In this sense, using polynomials to shape trajectories, and computing accelerations and other parameters via inverse dynamics, is an efficient approach to obtain suboptimal solutions. In this thesis the area of attitude manoeuvres is covered, as well as translational motions in the frame of docking to a tumbling satellite for Active Debris Removal missions (in which the detumbling case is also studied). In the case of attitude slew manoeuvres, quaternions are shaped with polynomials and normalised. Issues such as numerical stability of high-order polynomials and the special case of spin-to-spin manoeuvres have been addressed. Regarding trajectory optimisation, efficient algorithms for time minimisation are proposed, along with obstacle avoidance methods. The performance of the polynomial trajectories compared to optimal control is analysed. The polynomial motion planning method is applied to manoeuvres of exible spacecraft, assessing how the smoothness of motions can limit induced vibrations. In the scenario of docking to a tumbling target (based on Envisat), trajectories are generated with polynomials and fuel is optimised. An axisymmetric approximation of the target is used to analytically evaluate its dynamics. A cylindrical surface enclosing the target is defined for obstacle avoidance purposes. The docking strategy is divided in three segments (first approach, hovering, docking axis approach), to enhance safety and robustness. While in the attitude case the trajectory is tracked with a simple controller or performed in open-loop, in the docking scenario the feedback loop is closed by re-computing the trajectory planning algorithm with a certain frequency. Finally, the problem of detumbling the satellite is addressed. A concept is proposed based on an external module equipped with magnetorquers and carried by the chaser, which performs an autonomous docking to the target, and proceeds to stabilise its rotation. A preliminary design and sizing of the system is realised, and simulations are performed to assess its feasibility.