Owing to recent advancements in sensor technology, data mining, machine learning and cloud computation, structural health monitoring (SHM) based on a data-driven approach has gained more popularity and interest. The data-driven methodology has proved to be more efficient and robust compared with traditional physics-based methods. The past decade has witnessed remarkable progress in machine learning, especially in the field of deep learning which are effective in many tasks and has achieved state-of-the-art results in various engineering domains. In the same manner, deep learning has also revolutionized SHM technology by improving the effectiveness and efficiency of models, as well as enhancing safety and reliability. To some extent, it has also paved the way for implementing SHM in real-world complex civil and mechanical infrastructures. However, despite all the success, deep learning has intrinsic limitations such as its massive-labelled data requirement, inability to generate consistent results and lack of generalizability to out-of-sample scenarios. Conversely, in SHM, the lack of data corresponding to a different state of the structure is still a challenging task. Recent development in physics-informed machine learning methods has provided an opportunity to resolve these challenges in which limited-noisy data and mathematical models are integrated through machine learning algorithms. This method automatically satisfies physical invariants providing better accuracy and improved generalization. This manuscript presents the sate of- -the-art review of prevailing machine learning methods for efficient damage inspection, discuss their limitations, and explains the diverse applications and benefits of physics-informed machine learning in the SHM setting. Moreover, the latest data extraction strategy and the internet of things (IoT) that support the present data-driven methods and SHM are also briefly discussed in the last section.