Large earthquakes often do not occur on a simple planar fault but involve rupture of multiple geometrically complex faults. The 2016 Mw 7.8 Kaikoura earthquake, New Zealand, involved the rupture of at least 21 faults, propagating from southwest to northeast for about 180 km. Here we combine space geodesy and seismology techniques to study subsurface fault geometry, slip distribution, and the kinematics of the rupture. Our finite-fault slip model indicates that the fault motion changes from predominantly right-lateral slip near the epicenter to transpressional slip in the northeast with a maximum coseismic surface displacement of about 10 m near the intersection between the Kekerengu and Papatea faults. Teleseismic back projection imaging shows that rupture speed was overall slow (1.4 km/s) but faster on individual fault segments (approximately 2 km/s) and that the conjugate, oblique-reverse, north striking faults released the largest high-frequency energy. We show that the linking Conway-Charwell faults aided in propagation of rupture across the step over from the Humps fault zone to the Hope fault. Fault slip cascaded along the Jordan Thrust, Kekerengu, and Needles faults, causing stress perturbations that activated two major conjugate faults, the Hundalee and Papatea faults. Our results shed important light on the study of earthquakes and seismic hazard evaluation in geometrically complex fault systems.