Venus does not generate its own global magnetic field, but the solar wind—the constant stream of charged particles from the Sun—induces a magnetic field around the planet. Using data from the Venus Express spacecraft, we created a high-resolution map of this induced magnetic field under different solar wind conditions. We introduced a new mapping method that can make the best use of uneven spacecraft data, giving the highest resolution where the spacecraft collected the most observations. This allowed us to study structures as small as the ionopause (the boundary between the solar wind and the Venus atmosphere) and as large as the global draping of the solar wind magnetic field around the planet. We also found that two unusual magnetic features near the terminator and in the magnetotail change depending on the direction of the solar wind electric field. Our results help explain how these magnetic features form and provide guidance for improving computer models of Venus’s upper atmosphere.