The idea of describing the compression of an atom by placing it in a box with impenetrable walls dates back to the very early days of quantum chemistry and was first studied by Michels et. al in 1937 in an approximate manner. Soon after, the problem was solved formally for the confined hydrogen atom by Sommerfeld and Welker. Since then, this approach has continuously been extended to study atoms and small molecules under compression, as well as to model atoms in molecular cages such as fullerenes or zeolites. Considering the amount of research conducted throughout the past 85 years, a comprehensive and in-depth analysis of all methods would certainly exceed the limits of this review. We here aim to give a non-exhaustive overview over the basic ideas and highlight the series "Theory of Confined Quantum Systems" in Advances in Quantum Chemistry for an excellent collection of detailed reviews on the field. The hard-walled box, as introduced by Michels, takes the form of an impenetrable sphere with radius r C around the center of mass and may be described by adding the external potential V ext (r) to the Hamiltonian