This review is devoted to an investigation of the physical properties of the vacuum of quantum electrodynamics, making use of the perturbative-effective action approach. The effect of probing the vacuum with external perturbations is considered, and 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, some of which are described in 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 the full quantum theory to quantum-induced nonlinear electrodynamics, with a variety of applications to light propagation, photon splitting, and light-by-light scattering. Special emphasis is put on systems at finite temperature.