The design of obstetrical suction cups used for Vacuum Assisted Delivery (VAD) has not substantially evolved through history despite of its inherent limitations. The associated challenges concern both the decrease of risk of soft tissue damage and failure of instrumental delivery due to detachment of the cup. The present study firstly details some of the suction-based strategies that have been developed in wildlife in order to create and maintain an adhesive contact with potentially rough and uneven substratum in dry or wet environments. Such strategies have permitted the emergence of bioinspired suction-based devices in the fields of robotics or biomedical patches that are briefly reviewed. The objective is then to extend the observations of such suction-based strategies towards the development of innovative medical suction cups. We firstly conclude that the overall design, shape and materials of the suction cups could be largely improved. We also highlight that the addition of a patterned surface combined with a viscous fluid at the interface between the suction cup and scalp could significantly limit the detachment rate and the differential pressure required to exert a traction force. In the future, the development of a computational model including a detailed description of scalp properties should allow to experiment various designs of bioinspired suction cups.