The confluence of our ability to handle big data, significant increases in instrumentation density and quality, and rapid advances in machine learning (ML) algorithms have placed Earth Sciences at the threshold of dramatic progress. ML techniques have been attracting increased attention within the seismic community, and, in particular, in microseismic monitoring where they are now being considered a game-changer due to their real-time processing potential. In our review of the recent developments in microseismic monitoring and characterisation, we find a strong trend in utilising ML methods for enhancing the passive seismic data quality, detecting microseismic events, and locating their hypocenters. Moreover, they are being adopted for advanced event characterisation of induced seismicity, such as source mechanism determination, cluster analysis and forecasting, as well as seismic velocity inversion. These advancements, based on ML, include by-products often ignored in classical methods, like uncertainty analysis and data statistics. In our assessment of future trends in ML utilisation, we also see a strong push toward its application on distributed acoustic sensing (DAS) data and real-time monitoring to handle the large amount of data acquired in these cases.