The placenta is both the literal and metaphorical black box of pregnancy. Measurement of the function of the placenta has the potential to enhance our understanding of this enigmatic organ and serve to support obstetric decision making. Advanced imaging techniques are key to supporting these measurements. This review summarises emerging imaging technology being used to measure the function of the placenta and new developments in the computational analysis of this data. We address three important examples where functional imaging is supporting our understanding of these conditions: fetal growth restriction, placenta accreta, and twin-twin transfusion syndrome.