Increasing use of renewable energy sources, liberalized energy markets and most importantly, the integrations of various monitoring, measuring and communication infrastructures into modern power system network offer the opportunity to build a resilient and efficient grid. However, it also brings about various threats of instabilities and security concerns in form of cyberattack, voltage instability, power quality (PQ) disturbance among others to the complex network. The need for efficient methodologies for quicker identification and detection of these problems have always been a priority to energy stakeholders over the years. In recent times, machine learning techniques (MLTs) have proven to be effective in numerous applications including power system studies. In the literature, various MLTs such as artificial neural networks (ANN), Decision Tree (DT), support vector machines (SVM) have been proposed, resulting in effective decision making and control actions in the secured and stable operations of the power system. Given this growing trend, this paper presents a comprehensive review on the most recent studies whereby MLTs were developed for power system security and stability especially in cyberattack detections, PQ disturbance studies and dynamic security assessment studies. The aim is to highlight the methodologies, achievements and more importantly the limitations in the classifier(s) design, dataset and test systems employed in the reviewed publications. A brief review of reinforcement learning (RL) and deep reinforcement learning (DRL) approaches to transient stability assessment is also presented. Finally, we highlighted some challenges and directions for future studies.