We illustrate some fundamental alterations of the solar wind-magnetosphere interaction that occur during low Mach number solar wind. We first show that low Mach number solar wind conditions are often characteristic of coronal mass ejections (CMEs) and magnetic clouds in particular. We then illustrate the pivotal role of the magnetosheath. This comes from the fact that low Mach number solar wind leads to the formation of a low thermal β magnetosheath downstream of the bow shock. This property influences magnetic forces and currents, in particular, and in turn alters magnetosheath-magnetosphere coupling. The implications of this unusual regime of interaction have generally been overlooked. Potentially affected phenomena include the following: (1) asymmetric magnetosheath flows (with substantial enhancements), (2) asymmetric magnetopause and magnetotail shapes, (3) changes in the development of the Kelvin-Helmholtz instability and giant spiral auroral features, (4) variations in the controlling factors of dayside magnetic reconnection, (5) cross polar cap potential saturation and Alfvén wings, and (6) global sawtooth oscillations. Here we examine these phenomena, primarily by use of global magnetohydrodynamic simulations, and discuss the mechanisms that rule such an altered interaction. We emphasize the fact that all these effects tend to occur simultaneously so as to render the solar wind-magnetosphere interaction drastically different from the more typical high Mach number case. In addition to the more extensively studied inner magnetosphere and magnetotail processes, these effects may have important implications during CME-driven storms at Earth, as well as at other astronomical bodies such as Mercury.