Baffin Bay is an Arctic basin between Canada and Greenland, connected via Davis Strait with the Labrador Sea in the south. Due to its shallow water depth of only 500 m, Davis Strait acts as a gateway for the Arctic water exchange between Baffin Bay and the Atlantic. The nature of Baffin Bay and Davis Strait crust has long been a subject of debate. Either oceanic or stretched continental crust have been proposed by different authors from sonobuoy readings, seismic reflection and potential field data. We here present the new results of two seismic refraction lines acquired with ocean bottom seismometers. P-wave velocity models for both lines are constrained and complemented by density models, seismic reflection and magnetic anomaly data. Line AWI-20080500/AWI-20100400, in southern Baffin Bay, is oriented across a proposed Eocene spreading centre. This line confirms the existence of oceanic crust in southern Baffin Bay and allows for a regional mapping of the oceanic crust. With a plate kinematic model we depict the evolution of this basin and can distinguish between Palaeocene and Eocene oceanic crust. Line AWI-20080700 in Davis Strait crosses the Ungava Fault Complex, a major transform fault, where extension was followed by a stage of transpression. We here find deformed blocks of continental crust that are separated by transform faults of the Ungava Fault Complex. Between these blocks a region of 50 km is characterized by high P-wave velocities and a thin crust that we interpret as stretched and highly intruded crust. Tectonic modelling depicts a great lateral movement of 310 km of the continental blocks along the Ungava Fault complex. The compressional component is visible in a 70 km wide overlap of crust that had to be compensated by deformation of the blocks. With our new models and the compilation of published Moho depth and seismic stratigraphy we try to estimate the paleo bathymetry and the role of Davis Strait as a polar gateway.