The recent advancements in robotics and autonomous systems have shown a significant shift towards integrating sophisticated planning and optimization techniques to enhance performance in complex and dynamic environments. A notable trend is the use of advanced machine learning models, particularly transformers, to improve the efficiency and accuracy of path planning and task execution. These models are being leveraged to handle the complexities of real-time decision-making, especially in scenarios involving multiple agents, dynamic obstacles, and constrained environments. Additionally, there is a growing emphasis on the integration of active sensing with rearrangement planning to enable more efficient object retrieval from cluttered spaces. This approach combines heuristic-based sensing with Monte-Carlo Tree Search for retrieval planning, demonstrating superior performance in both simulated and real-world scenarios. Another emerging area is the application of differentiable optimization frameworks, which are being parallelized on GPUs to handle the high computational demands of task and motion planning. These frameworks offer a scalable solution to the challenges posed by non-convex constraints and local optima, as evidenced by their successful deployment in high-dimensional robotic systems. Furthermore, the field is witnessing innovative solutions for long-lived robot operations in large-scale environments, where anticipatory planning is used to optimize task sequences by considering future impacts of current actions. This approach, combined with graph neural networks, shows promise in scaling to realistic environments. Notably, pseudospectral techniques and geometric heat flow equations are being employed to rapidly generate optimal trajectories for high-dimensional systems, significantly reducing computational time while adhering to constraints. These developments collectively indicate a move towards more intelligent, adaptive, and efficient robotic systems capable of operating in diverse and unpredictable settings.