State management in Elixir can be achieved using processes, Agents, or stateful applications in Phoenix. Each process has its own state, allowing for isolation and concurrency.

Managing state in Elixir involves leveraging its process model, which provides a unique way of encapsulating state in lightweight, isolated processes. Each Elixir process can maintain its own state, which is stored in its memory and is not shared with other processes. This design promotes the principles of isolation and fault tolerance, allowing processes to crash without affecting the rest of the system. For more structured state management, Elixir offers the Agent module, which provides a simple way to create a process that holds state and exposes functions to read and update that state. This is particularly useful for maintaining shared state in applications while still adhering to the actor model. In the context of web development, state management can also be handled through the Phoenix framework, which allows for session storage, context management, and real-time updates through Channels. By employing these approaches, Elixir developers can effectively manage state in their applications, ensuring responsiveness and reliability.