This paper presents a comprehensive summary of recent advancements in motion planning under parametric uncertainties, focusing on the application of closed-loop state sensitivity. This concept provides a framework for quantifying how deviations in model parameters affect the behavior of a system in closed-loop, facilitating the generation of robust trajectories. Various methods have been proposed to improve the resilience of robotic systems to model inaccuracies. However, these approaches often face challenges such as computational complexity and limitations in real-time applications. This paper synthesizes key results from several recent works, highlighting the development of techniques that optimize trajectory robustness while reducing computational overhead. Additionally, we outline the practical applications of these methods, discussing their validation through simulations and experiments on robotic systems subject to non-negligible uncertainties in their models.