Abstract: We will review a formalism for real time evolution in quantum theory in the semiclassical limit, using the path integral. The motivation is to understand non-perturbative transitions in QFT in situations with interesting time dependence. We will illustrate how it works for the decay of a coherent state trapped in a metastable region in quantum mechanics. At the end we briefly speculate on the extension to QFT. Based on [2603.06575], [2605.04139]