This survey paper provides a comprehensive review of recent advances in reinforcement learning (RL) applied to finance. It begins with a thorough introduction to Markov decision processes (MDPs), the foundational framework for RL, covering both infinite and finite time horizons, as well as linear MDPs and functional approximation. The paper then details model-free RL algorithms, focusing on value-based methods (e.g., Q-learning, SARSA) and policy-based methods (e.g., REINFORCE, actor-critic), and explains how deep neural networks extend these to deep RL. The core of the survey examines six key financial applications: optimal execution, portfolio optimization, option pricing and hedging, market making, smart order routing, and robo-advising. For each application, the paper discusses the underlying models, how RL is applied, and the advantages over classical stochastic control approaches, such as reduced model assumptions and the ability to leverage large datasets. The survey concludes by highlighting future research directions, including multi-agent RL, inverse RL, and explainable RL, emphasizing the potential for RL to transform quantitative finance.