Function calling APIs enable LLMs to output structured function invocations for external tool execution. Mechanism: Provide function schemas (name, parameters, types), model decides when to call functions, outputs structured JSON with function name and arguments, application executes function and returns results. OpenAI format: functions array with JSON Schema definitions, model returns function_call with name and arguments. Use cases: Database queries, API calls, calculations, file operations, web searches, any external capability. Best practices: Clear function descriptions, typed parameters, handle missing/malformed calls, validate arguments before execution. Parallel function calling: Some models output multiple calls simultaneously. Forced vs optional: Can require function use or let model decide. Security considerations: Validate and sanitize arguments, limit function capabilities, audit function calls. Alternatives: ReAct pattern with text parsing, tool tokens, structured generation. Evolution: Tool use increasingly native to models - Claude, GPT-4, Gemini all support robust function calling. Foundation for AI agents and autonomous systems.