The seminar will explore the evolving capabilities of large language models (LLMs) in reasoning (e.g. mathematical and common-sense reasoning), and planning and decision-making (e.g. decomposition into simpler sub-tasks and planning for performing a complex task). It will highlight recent advancements and address emerging challenges by examining techniques such as reinforcement learning, post-training optimization, and inference-time scaling. Additionally, the seminar will focus on developing robust benchmarks, expanding LLMs to multi-modal and embodied environments, and integrating them into agentic systems. We will assess the opportunities, risks and limitations of using LLMs as reasoners and planners, with an aim to provide valuable insights and guidance for further advancements in LLM-based reasoning and planning methodologies.