I. Introduction  
II. Preliminaries  
III. Traditional HJ Reachability for Learned Controls  
IV. Learning Reachability in Model-free Settings  
V. Solving Reach-Avoid Problems  
VI. Model-free Safe Reinforcement Learning  
VII. Robustness and Real-World Settings  
VIII. Limitations and Remaining Challenges  
IX. Future Research Directions  
X. Conclusion  