The Interstellar Boundary Explorer (IBEX) has provided the first energy-resolved all-sky maps of energetic neutral atom (ENA) emissions from the heliosphere's boundary with the local interstellar medium (LISM). The IBEX maps reveal, superposed on a global ENA background, an enigmatic “ribbon” of enhanced ENA emission, a feature unpredicted by theory and numerical simulations and requiring a new paradigm for the heliosphere/LISM interaction. The ribbon appears to be ordered by the interstellar magnetic field; it is up to ∼3 times brighter than the background emission and spectrally distinct from it. The ribbon's origin, whether inside or outside the heliopause or at more exotic locations in the LISM, is unknown. Here, we review the various hypotheses that have been proposed to explain the ribbon as well as what we have learned from the IBEX sky maps about the ENAs' parent ion populations and about the structure, dynamics, and properties of the outer heliosphere and nearby interstellar medium. We conclude with a brief mention of new IBEX results on lunar and magnetospheric ENAs and a preview of a possible future mission that builds on the successes of IBEX as we continue to explore our home in the galaxy.