Venus lacks a significant intrinsic magnetic field, and thus, its atmosphere and ionosphere interact directly with the solar wind flow and magnetic field from the Sun. Interplanetary magnetic fields (IMF) can penetrate into the ionosphere when the upstream solar wind dynamic pressure is stronger than the ionospheric plasma pressure. Magnetic topology can be inferred at Venus if it is defined as the magnetic connectivity to the collisional atmosphere/ionosphere, rather than connectivity to the planet’s surface. Magnetic topology can be inferred from the pitch angle and energy distribution of superthermal (> ~1 eV) electrons. More specifically, the presence of loss cones in electron pitch angle distributions infers connectivity to the nightside collisional atmosphere and the presence of ionospheric photoelectrons (identified from electron energy distributions) indicates connectivity to the dayside collisional ionosphere. We design automated procedures to determine magnetic topology with electron and magnetic field measurements by the Venus Express spacecraft over its entire mission (2006-2014). This allows us to provide the first statistical mapping of magnetic topology at Venus. We also examine how the upstream drivers affect the low-altitude magnetic topology, revealing different magnetized states of the Venus ionosphere. We find that open and closed (a surprising topology not expected at Venus) fields cluster around the terminator and draped fields dominate other regions. Our results also reveal that there is more dayside magnetic connectivity in the -E (solar wind motional electric field) hemisphere than the +E hemisphere, and during solar maximum. During solar minimum, however, there is more nightside magnetic connectivity. Last but not the least, to understand the true nature of these magnetic topologies and broadly speaking the planet-solar wind interaction, we need to think about possible ways to measure the deeply penetrated magnetic fields at Venus and Mars.