Large language models have progressed from text predictors into the reasoning core of autonomous agents, systems that plan, invoke tools, maintain memory, and coordinate with other agents to pursue goals over long horizons. The resulting literature has grown explosively but unevenly, splitting into subcommunities that rarely cite one another. This survey imposes a function-first taxonomy that organizes the field by the architectural role each component plays rather than by the framework that introduced it: four component pillars (planning and reasoning, memory, tool use, and multi-agent coordination) grounded in two context dimensions (interactive environments and application domains) and assessed along two cross-cutting concerns, evaluation and safety, which we treat as first-class pillars rather than afterthoughts. Synthesizing more than two hundred works from 2021 through early 2026, including the reasoning-native models, computer-use agents, and agent-security research absent from earlier surveys, we find a field pulling in two directions: its components are consolidating, as prompting gives way to trained reasoning and scaffolds migrate into the models, while its frontier, grounding agents in real environments, evaluating them honestly for cost and reliability, and defending them against attack, remains wide open. Throughout, we give documented negative results on self-correction, multi-agent debate, and agentic scaffolding equal weight with positive claims, support the argument with small controlled experiments of our own, and show that capability and safety are distinct axes that must be measured apart. A continuously updated reading list of the surveyed papers is maintained at https://github.com/js-lee-AI/awesome-llm-agent-papers.