Conventional damage detection techniques are gradually being replaced by state-of-the-art smart monitoring and decision-making solutions. Near real-time and online damage assessment in structural health monitoring (SHM) systems is a promising transition toward bridging the gaps between the past's applicative inefficiencies and the emerging technologies of the future. In the age of the smart city, Internet of Things (IoT), and big data analytics, the complex nature of data-driven civil infrastructures monitoring frameworks has not been fully matured. Machine learning (ML) algorithms are thus providing the necessary tools to augment the capabilities of SHM systems and provide intelligent solutions for the challenges of the past. This article aims to clarify and review the ML frontiers involved in modern SHM systems. A detailed analysis of the ML pipelines is provided, and the in-demand methods and algorithms are summarized in augmentative tables and figures. Connecting the ubiquitous sensing and big data processing of critical information in infrastructures through the IoT paradigm is the future of SHM systems. In line with these digital advancements, considering the next-generation SHM and ML combinations, recent breakthroughs in (1) mobile device-assisted, (2) unmanned aerial vehicles, (3) virtual/augmented reality, and (4) digital twins are discussed at length. Finally, the current and future challenges and open research issues in SHM-ML conjunction are examined. The roadmap of utilizing emerging technologies within ML-engaged SHM is still in its infancy; thus, the article offers an outlook on the future of monitoring systems in assessing civil infrastructure integrity.