Hylleraas' paper on the ground state of the helium atom represents the first ab initio calculation on a two-electron system in quantitative agreement with experiment. As such, it served not only as an important numerical verification of wave mechanics, it also exposed the shortcomings of determinantal expansions for accurate calculations of molecular and atomic electronic structure. By the simple addition of terms linear in the interelectronic distance, dramatic improvements in the description of the electronic wave function were achieved. The generalization to larger systems of chemical interest has proven difficult but interest in the techniques pioneered by Hylleraas has grown in recent years, prompted by progress in computer technology.