The plasma membrane surrounds every single cell and essentially shapes cell life by separating the interior from the external environment. Thus, maintenance of cell membrane integrity is essential to prevent death caused by disruption of the plasma membrane. To counteract plasma membrane injuries, eukaryotic cells have developed efficient repair tools that depend on Ca2+- and phospholipid-binding annexin proteins. Upon membrane damage, annexin family members are activated by a Ca2+ influx, enabling them to quickly bind at the damaged membrane and facilitate wound healing. Our recent studies, based on interdisciplinary research synergy across molecular cell biology, experimental membrane physics, and computational simulations show that annexins have additional biophysical functions in the repair response besides enabling membrane fusion. Annexins possess different membrane-shaping properties, allowing for a tailored response that involves rapid bending, constriction, and fusion of membrane edges for resealing. Moreover, some annexins have high affinity for highly curved membranes that appear at free edges near rupture sites, a property that might accelerate their recruitment for rapid repair. Here, we discuss the mechanisms of annexin-mediated membrane shaping and curvature sensing in the light of our interdisciplinary approach to study plasma membrane repair.