Although the analytic solution of the wave function for the isolated hydrogen atom played a pivotal role in establishing the new quantum theory during the early part of the twentieth century, no corresponding solutions exist for systems with three or more charged particles. A complete solution of the three-body Coulomb problem requires a solution of Schrödinger's wave equation for a function that gives the probability that three charged particles are moving away from each other with precisely specified energies and directions. The three-body Coulomb problem plays a central role in understanding the physics of collisional ionization, a basic process that underlies many physical phenomena, from the glow of fluorescent lights to the chemistry of interstellar gases. Recently, a computational framework for solving ionization problems has been provided, and supercomputers have been used to produce numerical solutions of the ionization of a hydrogen atom by electron impact that reveal the full dynamics of this problem.