Simulations of energetic neutral atom (ENA) maps predict flux magnitudes that are, in some cases, similar to those observed by the Interstellar Boundary Explorer (IBEX) spacecraft, but they miss the ribbon. Our model of the heliosphere indicates that the local interstellar medium (LISM) magnetic field (BLISM) is transverse to the line of sight (LOS) along the ribbon, suggesting that the ribbon may carry its imprint. The force-per-unit area on the heliopause from field line draping and the LISM ram pressure is comparable with the ribbon pressure if the LOS approximately 30 to 60 astronomical units and BLISM approximately 2.5 microgauss. Although various models have advantages in accounting for some of the observations, no model can explain all the dominant features, which probably requires a substantial change in our understanding of the processes that shape our heliosphere.