In contemporary theories of the structure of matter at very short distance scales, various properties (some of them hypothetical as yet) of the vacuum are of crucial importance. The technical framework for such studies is quantum field theory. The aim of this article is to provide access, for a non-specialist readership, to the physics of the vacuum as presently understood in quantum field theory. To do this, heavy reliance is placed on a fundamental analogy. The basic theoretical entity—the quantum field—is here regarded as analogous to a quantum-mechanical system with (infinitely) many degrees of freedom. A system of interacting quantum fields is then analogous to a complicated system in solid state physics; it can exist in different energy states, namely the ground state and various excited states. The excited states of the field system are characterized by the presence of excitation quanta, which are the particles (electrons, quarks, photons…) of which our material world is composed. In the ground state of the field system there are no excitation quanta, and hence no particles, present: the vacuum is this ground state. Consequently, different features of the vacuum may be modelled by the ground states of various appropriate solid state systems. For example, the vibrational ground state of a crystal models the electromagnetic field vacuum, a semiconductor models the Dirac vacuum, and superconductors may model aspects of the vacuum as regards the strong and weak forces. These and other models are used in qualitative discussions of many phenomena which involve the properties and structure of the vacuum: for example, spontaneous emission and the Lamb shift, pair creation and the associated screening of charge by vacuum polarization, the origin of mass for the W and Z bosons, and the confinement of quarks. Finally, several of the themes are gathered together in a brief introduction to the hypothesis that the universe itself is the grossly inflated result of a vacuum fluctuation.