Markov Decision Processes (MDPs) are solved using methods like dynamic programming, which provides systematic algorithms based on the Bellman equations to find optimal policies. A key approach within dynamic programming is value iteration, where the algorithm iteratively updates the value of each state by applying the Bellman optimality equation until the values converge, ensuring the policy derived from these values is optimal. Another dynamic programming technique is policy iteration, which alternates between policy evaluation (calculating the value of a given policy) and policy improvement (updating the policy based on these values) until it stabilizes. Both methods rely on the principle of optimality and require knowledge of the transition probabilities and rewards, making them computationally intensive but effective for small to medium-sized problems. For larger MDPs, approximate or reinforcement learning methods are often employed.