Security in power systems is of utmost importance to ensure the reliable and safe operation of electricity infrastructure. With the increasing integration of digital technologies and the advent of the smart grid, modern power systems infrastructure have become more interconnected and reliant on data communication networks. Nevertheless, they are also exposed to various cybersecurity threats and vulnerabilities at the same time.To solve the security problems mentioned above, this Ph.D. thesis aims to develop data-analytics methods for security-relevant problems in power systems. This thesis includes 2 aspects, namely dynamic security assessment and nonintrusive loading monitoring, where the common thread is to identify the abnormal situations and raise potential solutions. With a vast amount of real-time data collected and utilized in modern power systems, data-driven methods can be a powerful tool to deal with these problems for their computational efficiency. The techniques employed in this thesis involve anomaly detection (to detect cyberattacks, e.g., Long Short-Term Memory, Local Outlier Factor, etc.), interpretation analysis (to quantify the contributions of input features against the machine learning models, e.g., SHapley Additive exPlanations and Shapley Additive Global importancE), adversarial attacks and mitigation (to measure the model vulnerability), and ensemble learning (to enhance the reliability of the predictions).All the proposed methods have been well verified on simulations over the corresponding data sets recorded from power system operations. Throughout the data experiments, it is shown that proper employment of ML algorithms could efficiently solve the security-relevant problems in power systems, and interpretation analysis will help to better understand the internal operation modes of the trained ML models as well as identify these crucial data features that dominate the com-