These notes provide a pedagogical introduction to the theoretical study of vacuum polarization effects in strong electromagnetic fields as provided by state-of-the-art high-intensity lasers. Quantum vacuum fluctuations give rise to effective couplings between electromagnetic fields, thereby supplementing Maxwell's linear theory of classical electrodynamics with nonlinearities. Resorting to a simplified laser pulse model, allowing for explicit analytical insights, we demonstrate how to

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... y analyze all-optical signatures of these effective interactions in high-intensity laser experiments. Moreover, we highlight several key features relevant for the accurate planning and quantitative theoretical analysis of quantum vacuum nonlinearities in the collision of high-intensity laser pulses.