The development of scalable and real-time implementable trajectory generation algorithms for uncertain dynamical systems based on both model-based and data-driven stochastic optimal control methods can find applications in a wide range of real-world problems. The focus of this talk will be on trajectory optimization problems in which the boundary conditions correspond to probability distributions rather than fixed states. This class of stochastic trajectory generation problems admits in the most general case an infinite dimensional representation, which is computationally intractable. This research relies instead on finite-dimensional representations together with optimization techniques which exploit the structure of the problem. We will also talk about data-driven trajectory optimization algorithms, in which the time-evolution of the first two moments of the uncertain state of the system is described by means of either a combination of model based and machine learning methods (such as Gaussian processes) or completely data-driven and model-free methods which leverage data collected along the system's ensuing trajectory.