Abstract: Atmospheric turbulence is a key limiting factor for long-range optical imaging systems. The geometric distortion, dynamic blur, and contrast attenuation induced by it severely degrade the imaging quality and data interpretation efficiency in both military and civilian fields such as UAV reconnaissance, satellite remote sensing, and astronomical observation. This paper systematically reviews the research progress in the field of atmospheric turbulence imaging simulation and restoration. First, it analyzes the physical mechanism of turbulence-induced degradation, and clarifies the correspondence between spatial geometric distortion and frequency-domain phase perturbations (first-order tilt and high-order aberrations). Second, it sorts out the data support system, analyzes the characteristics and limitations of open-source datasets, and compares the trade-offs of data synthesis technologies such as spatial empirical modeling and phase-domain physical modeling. Subsequently, it deeply explores the evolution of restoration algorithms, pointing out the limitations of manually designed features in traditional methods and elucidating how deep learning achieves a performance leap through the integration of physics-inspired and data-driven approaches. Finally, it summarizes the core research challenges, including the scarcity of real-world data, synthetic-to-real domain shift, and insufficient algorithm generalization, and looks forward to future directions such as refined turbulence physical modeling, efficient restoration network design, and joint optimization of algorithm-optical hardware. This review can provide a valuable reference for theoretical research and engineering practices in atmospheric turbulence image restoration, and thereby facilitate breakthroughs in long-range optical imaging and detection technologies.