**This provides a comprehensive overview of using reinforcement learning (RL) to enhance the reasoning abilities of large language models (LLMs).** It contrasts conventional LLMs with newer reasoning models and highlights the potential of RL for strategic computation. The author explains key RL concepts like RLHF and PPO, then introduces more recent advancements such as GRPO and RLVR, exemplified by DeepSeek-R1's training. Finally, the article summarizes lessons from recent research papers, exploring topics like improving distilled models, addressing biases in RL algorithms, the emergence of reasoning capabilities, generalization across domains, and the ongoing debate about the primary drivers of LLM reasoning.