AI agentic programming is an emerging paradigm where large language model (LLM)-based coding agents autonomously plan, execute, and interact with tools such as compilers, debuggers, and version control systems. Unlike conventional code generation, these agents decompose goals, coordinate multi-step processes, and adapt based on feedback, reshaping software development practices. This survey provides a timely review of the field, introducing a taxonomy of agent behaviors and system architectures and examining relevant techniques for planning, context management, tool integration, execution monitoring, and benchmarking datasets. We highlight challenges of this fast-moving field and discuss opportunities for building reliable, transparent, and collaborative coding agents.