Event identification is increasingly recognized as crucial for enhancing the reliability, security, and stability of the electric power system. With the growing deployment of Phasor Measurement Units (PMUs) and advancements in data science, there are promising opportunities to explore data-driven event identification via machine learning classification techniques. This dissertation explores the potential of data-driven event identification through machine learning classification techniques. In the first part of this dissertation, using measurements from multiple PMUs, I propose to identify events by extracting features based on modal dynamics. I combine such traditional physics-based feature extraction methods with machine learning to distinguish different event types.Using the obtained set of features, I investigate the performance of two well-known classification models, namely, logistic regression (LR) and support vector machines (SVM) to identify generation loss and line trip events in two datasets. The first dataset is obtained from simulated events in the Texas 2000-bus synthetic grid. The second is a proprietary dataset with labeled events obtained from a large utility in the USA. My results indicate that the proposed framework is promising for identifying the two types of events in the supervised setting. In the second part of the dissertation, I use semi-supervised learning techniques, which make use of both labeled and unlabeled samples.I evaluate three categories of classical semi-supervised approaches: (i) self-training, (ii) transductive support vector machines (TSVM), and (iii) graph-based label spreading (LS) method. In particular, I focus on the identification of four event classes i.e., load loss, generation loss, line trip, and bus fault. I have developed and publicly shared a comprehensive Event Identification package which consists of three aspects: data generation, feature extraction, and event identification with limited labels using semi-supervised methodologies. Using this package, I generate eventful PMU data for the South Carolina 500-Bus synthetic network. My evaluation confirms that the integration of additional unlabeled samples and the utilization of LS for pseudo labeling surpasses the outcomes achieved by the self-training and TSVM approaches. Moreover, the LS algorithm consistently enhances the performance of all classifiers more robustly.