This paper summarizes recent advancements on spatio-temporal data-driven and machine learning methods for static and dynamic security assessment, and their particular use cases. It is a collective effort of different research groups members of the IEEE Working Group on Big Data Analytics for Transmission Systems, to provide transmission system operators (TSOs) with innovative tools and ideas for their potential implementation. The algorithms presented here are classified as non-training and training approaches, namely spatio-temporal and machine learning based, considering as input time series from time domain simulations, and or synchrophasor data from wide-area monitoring systems. The efficacy of these algorithms is then evaluated in different IEEE benchmark models and using real system measurements from different countries.