The Robot Operating System 2 (ROS~2) has emerged as a relevant middleware framework for robotic applications, offering modularity, distributed execution, and communication. In the last six years, ROS~2 has drawn increasing attention from the real-time systems community and industry. This survey presents a comprehensive overview of research efforts that analyze, enhance, and extend ROS~2 to support real-time execution. We first provide a detailed description of the internal scheduling mechanisms of ROS~2 and its layered architecture, including the interaction with DDS-based communication and other communication middleware. We then review key contributions from the literature, covering timing analysis for both single- and multi-threaded executors, metrics such as response time, reaction time, and data age, and different communication modes. The survey also discusses community-driven enhancements to the ROS~2 runtime, including new executor algorithm designs, real-time GPU management, and microcontroller support via micro-ROS. Furthermore, we summarize techniques for bounding DDS communication delays, message filters, and profiling tools that have been developed to support analysis and experimentation. To help systematize this growing body of work, we introduce taxonomies that classify the surveyed contributions based on different criteria. This survey aims to guide both researchers and practitioners in understanding and improving the real-time capabilities of ROS~2.