The Ulysses mission is the first to explore our heliosphere at all latitudes up to ¿80¿ and therefore is an ideal mission to study potential gradients in heliolatitude (and radial distance) of discontinuity occurrence rates and types. Directional discontinuities (DDs) are shown to be dependent on the type of solar wind streams that they are embedded in. The occurrence rate of DDs is 5--10 times higher in high-speed streams than in slow streams. The explanation is that nonlinear Alfv¿n waves dominate the high-speed streams and rotational discontinuities are the phase-steepened edges of the Alfv¿n waves. Dissipation at these phase-steepened Alfv¿n waves have been sought but not found. An e-(R-1)/5 decrease in discontinuity rate with increasing radial distance (R in units of AU) is partially an artifact of the selection criteria (discontinuity thickening), but dissipation at a relatively slow rate cannot be ruled out at this time. There is no obvious latitudinal gradients in discontinuity types or occurrence rates. Somewhat surprisingly, tangential discontinuities are detected at high latitudes. These have been associated with the edges of local small-scale magnetic decreases. A pair of slow shocks were detected at 5.3 AU. The speeds are similar to fast mode shock speeds. When Alfv¿n waves in high-speed streams impinge upon the Earth's magnetosphere, near-continuous substorms (called HILDCAAs) occur, leading to the pumping of an extraordinary amount of energy into the nightside ionosphere. Current discontinuity and Alfv¿n wave research problems are discussed. ¿ 1999 American Geophysical Union