Over the last several years there have been great improvements in the energy resolution and detection efficiency of angle-resolved photoemission spectroscopy. These improvements have made it possible to discover a number of fascinating features in the electronic structure of the high transition temperature (Tc) superconductors : apparently bandlike Fermi surfaces, flat-band saddle points, and nested Fermi surface sections. Recent work suggests that these features, previously thought explainable only by one-electron band theory, may be better understood with a many-body approach. Furthermore, other properties of the high-Tc superconductors, which are difficult to understand with band theory, are well described using a many-body picture. Angle-resolved photoemission spectroscopy has also been used to investigate the nature of the superconducting pairing state, revealing an anisotropic gap consistent with a d-wave order parameter and fueling the current debate over s-wave versus d-wave superconductivity.