Industrial internet of things (IIoT) has ushered us into a world where most machine parts are now embedded with sensors that collect data. This huge data reservoir has enhanced data-driven diagnostics and prognoses of machine health. With technologies like cloud or centralized computing, the data could be sent to powerful remote data centers for machine health analysis using artificial intelligence (AI) tools. However, centralized computing has its own challenges, such as privacy issues, long latency, and low availability. To overcome these problems, edge computing technology was embraced. Thus, instead of moving all the data to the remote server, the data can now transition on the edge layer where certain computations are done. Thus, access to the central server is infrequent. Although placing AI on edge devices aids in fast inference, it poses new research problems, as highlighted in this paper. Moreover, the paper discusses studies that use edge computing to develop artificial intelligence-based diagnostic and prognostic techniques for industrial machines. It highlights the locations of data preprocessing, model training, and deployment. After analysis of several works, trends of the field are outlined, and finally, future research directions are elaborated