In this study we describe a three-dimensional MHD model of the solar corona and heliosphere. We split the modeling region into two distinct parts: the solar corona (1 solar radius, RS, to 30 RS) and the inner heliosphere (30 RS to 5 AU). This combined model is driven solely by the observed line-of-sight photospheric magnetic field and can thus provide a realistic global picture of the corona and heliosphere for specific time periods of interest. We use the model to illustrate heliospheric structure during three different phases of the solar cycle: (1) Carrington rotation (CR) 1913 (August 22, 1996, to September 18, 1996), which occurred near solar minimum and overlapped the Whole Sun Month campaign; (2) CR 1892 (January 27, 1995, to February 23, 1995), which occurred during the declining phase of cycle 22 and coincided with the so-called Ulysses rapid latitude scan; and (3) CR 1947 (March 7, 1999, to April 4, 1999), which occurred approximately 15 months before the predicted maximum of solar cycle 23. We compare Ulysses and Wind observations with the simulation for CR 1913 and compare Ulysses observations during its traversal from pole to pole with CR 1892. We find that the simulations reproduce the overall large-scale features of the observations. We use the near-solar-maximum results to speculate on the structure of the high-latitude solar wind that Ulysses will encounter during its traversal of the southern and northern solar poles in 2000 and 2001, respectively. In particular, the results suggest that because of the presence of equatorial coronal holes the ordered pattern of corotating interaction region tilts and their associated shocks, which was observed during Ulysses' initial southward excursion in 1992, will likely disappear completely as Ulysses moves toward the south pole. We anticipate that Ulysses will encounter fast streams but will not remain within them for more than a fraction of a solar rotaton. Finally, the simulations suggest that crossings of the heliospheric current sheet will persist up to at least ~70¿ heliographic latitude. ¿ 2001 American Geophysical Union