Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. Finally, we identify emerging trends, such as domain-specific reasoning systems, and open challenges, such as evaluation and data quality. This survey aims to provide AI researchers and practitioners with a comprehensive foundation for advancing reasoning in LLMs, paving the way for more sophisticated and reliable AI systems. 1

Large Language Models (LLMs) have demonstrated impressive capabilities in complex reasoning tasks, yet they still struggle to reliably verify the correctness of their own outputs. Existing solutions to this verification challenge often depend on separate verifier models or require multi-stage self-correction training pipelines, which limit scalability. In this paper, we propose Policy as Generative Verifier (PAG), a simple and effective framework that empowers LLMs to self-correct by alternating between policy and verifier roles within a unified multi-turn reinforcement learning (RL) paradigm. Distinct from prior approaches that always generate a second attempt regardless of model confidence, PAG introduces a selective revision mechanism: the model revises its answer only when its own generative verification step detects an error. This verify-then-revise workflow not only alleviates model collapse but also jointly enhances both reasoning and verification abilities. Extensive experiments across diverse reasoning benchmarks highlight PAG's dual advancements: as a policy, it enhances direct generation and self-correction accuracy; as a verifier, its self-verification outperforms self-consistency.

Prevalent reinforcement learning~(RL) methods for fine-tuning LLM reasoners, such as GRPO or Leave-one-out PPO, abandon the learned value function in favor of empirically estimated returns. This hinders test-time compute scaling that relies on using the value-function for verification. In this work, we propose RL$^V$ that augments any ``value-free'' RL method by jointly training the LLM as both a reasoner and a generative verifier using RL-generated data, adding verification capabilities without significant overhead. Empirically, RL$^V$ boosts MATH accuracy by over 20\% with parallel sampling and enables $8-32\times$ efficient test-time compute scaling compared to the base RL method. RL$^V$ also exhibits strong generalization capabilities for both easy-to-hard and out-of-domain tasks. Furthermore, RL$^V$ achieves $1.2-1.6\times$ higher performance when jointly scaling parallel and sequential test-time compute with a long reasoning R1 model.

Verifiers or reward models are often used to enhance the reasoning performance of large language models (LLMs). A common approach is the Best-of-N method, where N candidate solutions generated by the LLM are ranked by a verifier, and the best one is selected. While LLM-based verifiers are typically trained as discriminative classifiers to score solutions, they do not utilize the text generation capabilities of pretrained LLMs. To overcome this limitation, we instead propose training verifiers using the ubiquitous next-token prediction objective, jointly on verification and solution generation. Compared to standard verifiers, such generative verifiers (GenRM) can benefit from several advantages of LLMs: they integrate seamlessly with instruction tuning, enable chain-of-thought reasoning, and can utilize additional inference-time compute via majority voting for better verification. We demonstrate that when using Gemma-based verifiers on algorithmic and grade-school math reasoning tasks, GenRM outperforms discriminative verifiers and LLM-as-a-Judge, showing a 16-64% improvement in the percentage of problems solved with Best-of-N. Furthermore, we show that GenRM scales favorably across dataset size, model capacity, and inference-time compute.