The Human Placenta Project has focused attention on the need for noninvasive magnetic resonance imaging (MRI)-based techniques to diagnose and monitor placental function throughout pregnancy. The hope is that the management of placenta-related pathologies would be improved if physicians had more direct, real-time measures of placental health to guide clinical decision making. As oxygen alters signal intensity on MRI and oxygen transport is a key function of the placenta, many of the MRI methods under development are focused on quantifying oxygen transport or oxygen content of the placenta. For example, measurements from blood oxygen level-dependent imaging of the placenta during maternal hyperoxia correspond to outcomes in twin pregnancies, suggesting that some aspects of placental oxygen transport can be monitored by MRI. Additional methods are being developed to accurately quantify baseline placental oxygenation by MRI relaxometry. However, direct validation of placental MRI methods is challenging and therefore animal studies and ex vivo studies of human placentas are needed. Here we provide an overview of the current state of the art of oxygen transport and quantification with MRI. We suggest that as these techniques are being developed, increased focus be placed on ensuring they are robust and reliable across individuals and standardized to enable predictive diagnostic models to be generated from the data. The field is still several years away from establishing the clinical benefit of monitoring placental function in real time with MRI, but the promise of individual personalized diagnosis and monitoring of placental disease in real time continues to motivate this effort.