The classical and quantum mechanical problem of a particle in the infinite circular well has recently surfaced in two quite different manifestations: (i) the observation of ‘‘electron standing waves’’ in circular ‘‘corrals’’ of atoms adsorbed on surfaces and (ii) as a benchmark example of an integrable system for comparison to the classical and quantum chaotic behavior of the ‘‘stadium billiards’’ problem. Motivated by this, we review the quantum and classical probability distributions for both position and momentum for this familiar problem, focusing on the visualization of the quantum wave functions and classical trajectories as well as the semiclassical connections between the two.