Launched in October 2008, NASA's Interstellar Boundary Explorer (IBEX) has provided the first-ever energy-resolved all-sky maps of energetic neutral atom (ENA) emissions from the boundary of the heliosphere with the local interstellar medium (LISM). The maps reveal an enigmatic "Ribbon" of enhanced emissions superposed on a smoothly varying global distribution of ENA emissions. The Ribbon lies between the locations where the two Voyagers crossed the termination shock and was not sampled by them on their trajectories out through the heliosphere. IBEX's discovery of the Ribbon-a feature completely unpredicted by theory and numerical simulations-requires a new paradigm in our understanding of the heliosphere/LISM interaction. The Ribbon appears to be ordered by the interstellar magnetic field and the solar wind's latitudinal structure. The Ribbon's origin, whether from processes occurring in the heliosphere or beyond in the LISM, is unknown and the subject of intense investigation. Continued observations over the first 3 years of the IBEX mission have characterized the Ribbon, including its location, energy spectra, fine structure, and time variations. Here we review and compare the various hypotheses that have been proposed to explain the Ribbon, assess their ability to account for the features that have emerged from 3 years of careful analysis of the IBEX sky maps, and discuss how evolving theories and observations during IBEX's extended mission and by the National Research Council's recommended follow-on mission (the Interstellar Mapping and Acceleration Probe) will be used to finally determine the true source of the Ribbon.