In Elixir, design patterns emerge from failures in production, reflecting distributed, concurrent, and fault-tolerant design principles.The actor model in Elixir treats each process as a living organism, facilitating asynchronous and failure-tolerant communication via messages.GenServer formalizes the actor pattern, providing structure, callbacks, and defined interaction APIs for building stateful services.Supervisors in Elixir introduce self-healing software by absorbing process failures with restart strategies like one_for_one and one_for_all.Task.async_stream enables concurrent, non-blocking processing of collections, preventing system overload with max_concurrency and timeout settings.The Application module in Elixir defines system behavior, emphasizing the lifecycle management and resilience hierarchy of processes.GenStateMachine models explicit state transitions in stateful systems, promoting clarity, testability, and behavior debugging.The Registry assigns names to live processes, offering global semantics for accessing and managing processes in distributed systems.The Repository pattern abstracts data persistence mechanics, decoupling core logic from storage details and facilitating testing and backend swapping.Context modules in Elixir provide semantic boundaries for system functions, offering composability, clarity, and refactoring flexibility.