The deterioration of civil infrastructure presents a critical economic and societal challenge, necessitating the development of advanced and efficient monitoring strategies. Artificial intelligence (AI) has recently emerged as a powerful tool for structural health monitoring (SHM) that considerably improves accuracy, robustness, and operational efficiency. Early AI applications focused predominantly on vibration-based monitoring, enabling automated and data-driven damage detection processes. As AI techniques have advanced, their scope has expanded to large-scale data analyses, thereby significantly enhancing predictive maintenance strategies. Trends toward the integration of AI with vision-based methods have recently increased, further advancing damage detection and facilitating the digital transformation of civil infrastructure monitoring. AI has also been instrumental in achieving precise structural displacement tracking and load assessment. This review critically examines the progression of AI in SHM by tracing its evolution from vibration-based methods to the incorporation of vision-based techniques, including damage detection, digital transformation, and measurement. Furthermore, this paper discusses the key challenges associated with deploying AI solutions in real-world environments while highlighting future research directions and potential innovations within this rapidly evolving field.