Magnetic fields are induced by the solar wind in the ionospheres of planets such as Venus and Mars, which possess only weak, or nonexistent, intrinsic magnetic fields. The magnetometer on the Pioneer Venus Orbiter (PVO) observed large-scale magnetic fields in the ionosphere when the solar wind dynamic pressure was high. During high solar wind dynamic pressure conditions the ionopause was observed to be broad and at low altitudes, whereas during low solar wind dynamic pressure conditions the ionopause was located at high altitudes (z>300 km) and was narrow (Δz≈20 km). We review the results of recent theoretical models of the magnetic field in the ionosphere of Venus, and, in particular, the one-dimensional MHD model of Shinagawa and Cravens (1988) and the two-dimensional kinematic dynamo model of Cravens et al. (1990). The results of these models are used as a starting point for an explanation of the behavior of the ionopause. It is well known that during low solar wind dynamic pressure conditions the location of the ionopause is determined by vertical pressure balance between the ionospheric thermal pressure and the magnetic pressure of the overlying magnetic barrier. The structure of the ionopause is not well understood; we suggest that the sensitivity of horizontal plasma transport to the presence of a magnetic field and the convergence of the vertical flow provide the explanation for the narrowness of the Venus ionopause. However, during high solar wind dynamic pressure conditions, ion-neutral friction also plays an important role in determining the thickness of the ionopause. ¿ American Geophysical Union 1991