Reinforcement learning (RL) has become central to LLM post-training, yet the methods that dominate current pipelines, PPO and GRPO, represent only a narrow slice of what RL offers. Understanding why these methods prevail, and what alternatives exist, requires a principled examination of the design decisions that underlie any RL algorithm. This survey organizes that examination around three stages of algorithm construction. We begin with MDP creation: how the reward function, state space, action space, termination condition, and discount factor are, or could be, defined for LLM training. We then turn to exploration, covering temperature sampling, entropy regularization, intrinsic motivation, tree search, and curriculum learning. Finally, we address learning along four classical RL dimensions: model-free versus model-based, value-based versus policy-based versus actor-critic, on-policy versus off-policy, and credit assignment, including both Monte Carlo methods, which rely on full return estimates, and bootstrapping methods, which update estimates using other learned predictions. Mapping the LLM literature onto this taxonomy reveals a strikingly non-uniform distribution of research effort. Critic-free policy gradients and Monte Carlo credit assignment are densely populated, while value-based methods, off-policy actor-critic training, and bootstrapping-based credit assignment remain largely unexplored despite well-established counterparts in classical RL. These gaps represent concrete opportunities for transferring proven RL techniques to LLM training. By making these gaps explicit alongside the methods that have proven effective, this survey offers researchers in both RL and LLMs a shared framework for understanding current practice and identifying promising directions for future work.

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