Real-time health monitoring of civil infrastructures is performed to maintain their structural integrity, sustainability, and serviceability for a longer time. With smart electronics and packaging technology, large amounts of complex monitoring data are generated, requiring sophisticated artificial intelligence (AI) techniques for their processing. With the advancement of technology, more complex AI models have been applied, from simple models to sophisticated deep learning (DL) models, for structural health monitoring (SHM). In this article, a comprehensive review is performed, primarily on the applications of AI models for SHM to maintain the sustainability of diverse civil infrastructures. Three smart data capturing methods of SHM, namely, camera-based, smartphone-based, and unmanned aerial vehicle (UAV)-based methods, are also discussed, having made the utilization of intelligent paradigms easier. UAV is found to be the most promising smart data acquisition technology, whereas convolution neural networks are the most impressive DL model reported for SHM. Furthermore, current challenges and future perspectives of AI-based SHM systems are also described separately. Moreover, the Internet of Things (IoT) and smart city concepts are explained to elaborate on the contributions of intelligent SHM systems. The integration of SHM with IoT and cloud-based computing is leading us towards the evolution of future smart cities.