  The GW approximation in electronic structure theory has become a widespread
tool for predicting electronic excitations in chemical compounds and materials.
In the realm of theoretical spectroscopy, the GW method provides access to
charged excitations as measured in direct or inverse photoemission
spectroscopy. The number of GW calculations in the past two decades has
exploded with increased computing power and modern codes. The success of GW can
be attributed to many factors: favorable scaling with respect to system size, a
formal interpretation for charged excitation energies, the importance of
dynamical screening in real systems, and its practical combination with other
theories. In this review, we provide an overview of these formal and practical
considerations. We expand, in detail, on the choices presented to the scientist
performing GW calculations for the first time. We also give an introduction to
the many-body theory behind GW, a review of modern applications like molecules
and surfaces, and a perspective on methods which go beyond conventional GW
calculations. This review addresses chemists, physicists and material
scientists with an interest in theoretical spectroscopy. It is intended for
newcomers to GW calculations but can also serve as an alternative perspective
for experts and an up-to-date source of computational techniques.
