## TL;DR
Reasoning models like OpenAI o1/o3 and DeepSeek-R1 represent a paradigm shift: instead of answering immediately, they "think" through problems via internal chain-of-thought, scaling inference-time compute for dramatically better math, coding, and scientific reasoning.

## Core Explanation
Standard LLMs (GPT-4, Claude) produce answers token-by-token with equal compute per token. Reasoning models allocate variable compute: easy questions get quick answers; hard problems trigger extended internal reasoning (hundreds to thousands of tokens). This mimics how humans spend more time on harder problems.

## Detailed Analysis
o1 launched September 2024; o3 (December 2024) achieved 87.5% on ARC-AGI benchmark. DeepSeek-R1 proved open-weight models can match closed reasoning through pure RL training — no human reasoning demonstrations needed. Google Gemini 2.0 Flash Thinking and Anthropic's extended thinking mode followed, making reasoning a standard LLM capability by 2025.

## Further Reading
- OpenAI: o1/o3 System Cards
- DeepSeek-R1 GitHub
- ARC Prize: Reasoning Benchmark