This paper develops the feature-based methods with physical interpretations to identify events in the power system. Two approaches to identifying single and successive events, respectively, are introduced. Since the subspace of the spatial-temporal blocks of synchrophasor data matrix represents the system dynamics compactly, we propose a dictionary-based method to identify the type of an event using one second of data. To address the challenge of identifying successive events with overlapping impacts, we propose a prediction-subtraction process to reduce the impact of a previous event. We propose to use the dominant eigenvalues of the system state matrix and the dominant singular values of the data matrix as the extracted features of individual events and train a convolutional neural network (CNN) classifier offline. This CNN classifier is used to identify the type of each of the successive events in real time. Both the recorded PMU data and simulated datasets validate the effectiveness of the proposed methods.