The field of optimization and planning is experiencing a significant shift with the integration of large language models (LLMs). Recent developments have demonstrated the potential of LLMs to enhance the efficiency, transparency, and adaptability of heuristic evolution, path planning, and trajectory planning. The use of LLMs has been shown to improve the performance of traditional methods, such as genetic programming and A*, by generating high-quality heuristics, waypoints, and constraint rules. Additionally, LLMs have been used to enable knowledge transfer and preference-aware heuristic generation across related tasks. Notable papers in this area include EvoSpeak, which integrates GP with LLMs to enhance the efficiency and interpretability of heuristic evolution. The $1000x Faster LLM-enhanced Algorithm For Path Planning in Large-scale Grid Maps proposes an innovative LLM-enhanced algorithm that achieves significant speedup and memory savings compared to existing methods. Other noteworthy papers include Work Zones challenge VLM Trajectory Planning, Simulation to Rules: A Dual-VLM Framework for Formal Visual Planning, and VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems. These papers demonstrate the potential of LLMs to advance the state-of-the-art in optimization and planning, and highlight the promise of automated heuristics discovery and formal visual planning.