Traditional power system stability assessment based on full model computation shows its drawbacks in real-time applications where fast variations are present at both demand side and supply side. This work presents the use of data mining techniques, in particular the Decision Trees (DTs), for fast evaluation of power system oscillatory stability and voltage stability from synchrophasor measurements. A regression tree-based approach is proposed to predict the stability margins. Modal analysis and continuation power flow are the tools used to build the knowledge base for off-line DT training. Corresponding metrics include the damping ratio of critical electromechanical oscillation mode and MW-distance to the voltage instability region. Classification trees are used to group an operating point into predefined stability state based on the value of corresponding stability indicator. A novel methodology for knowledge base creation has been elaborated to assure practical and sufficient training data. Encouraging results are obtained through performance examination. The robustness of the proposed predictor to measurement errors and system topological variations is analyzed. A scheme has been proposed to tackle the problem of when and how to update the data mining tool for seamless online stability monitoring. The optimal placement for the phasor measurement units (PMU) based on the importance of DT variables is suggested. A measurement-based voltage stability index is proposed and evaluated using field PMU measurements. It is later revised to evaluate the impact of wind generation on distribution system voltage stability. Next, a new data mining tool, the Probabilistic Collocation Method (PCM), is presented as a computationally efficient method to conduct the uncertainty analysis. As compared with the traditional Monte Carlo simulation method, the collocation method could provide a quite accurate approximation with fewer simulation runs. Finally, we show how to overcome the disadvantages of mode meters and ringdown analyzers by using DTs to directly map synchrophasor measurements to predefined oscillatory stability states. The proposed measurement-based approach is examined using synthetic data from simulations on IEEE test systems, and PMU measurements collected from field substations. Results indicate that the proposed method complements the traditional model-based approach, enhancing situational awareness of control center operators in real time stability monitoring and control.