The review is devoted to an investigation of the physical vacuum properties of quantum electrodynamics (QED), relying on the perturbative effective action approach. By probing the vacuum with external perturbations, its response is analyzed after averaging over the high-energy degrees of freedom. The book is written for scientists active in the field as well as for students who want to become familiar with the more advanced computational strategies of external-field problems which are partly outlined in great detail. Schwinger's proper-time method is the backbone of the book. Many recent results are presented, while others which are widespread in the literature are rederived in a unifying and compact way. The book ranges from full quantum theory to quantum-induced non-linear electrodynamics with its variety of applications to light propagation, photon splitting and light-by-light scattering. A special emphasis is put on systems at finite temperature.