In this talk, I will describe a learning-based data-driven approach for uncertainty propagation and reachability analysis that can be applied to general dynamical systems and provide results applying the methods to power systems. The problem of uncertainty propagation and quantification is of interest across the various discipline of science and engineering. The problem of uncertainty propagation and reachability analysis is complicated due to the nonlinear nature of dynamics involved in these applications. To address these challenges, I will present an approach that relies on the linear lifting of a nonlinear system provided by linear Perron-Frobenius (P-F) and Koopman operators. While the P-F operator propagates uncertainty or probability density function under the system dynamics, the Koopman operator propagates observables. These operators, therefore, provide a natural framework for the representation and propagation of uncertainty. By exploiting duality between P-F and Koopman operator, I will demonstrate how the finite dimensional approximations of P-F and Koopman operators can be used to propagate the moments of the probability density function that describes the uncertainty in the states. Furthermore, as only time-series data is used for the finite-dimensional approximation of the linear operators, the data-driven approach for moment propagation can be performed in a non-intrusive manner by only using the results from a black-box simulator with the system dynamics. The proposed approach effectively leverages the offline learning + online evaluation paradigm for very fast uncertainty propagation. To validate the methodology, simulations on nonlinear dynamical systems and power systems are performed and the proposed methodology demonstrated a speedup of 2-3 orders of magnitude compared to Monte-Carlo approaches.