Partially automated vehicle technology is increasingly common on-road. While this technology can provide safety benefits to drivers, it also introduces new concerns about driver attention. In particular, during partially automated driving, drivers are expected to stay vigilant so they can readily respond to important events in their environment. However, using partially automated vehicles on the highway places drivers in monotonous situations and requires them to do very little. This can place the driver in a state of cognitive underload in which (...) they experience a very small amount of cognitive demand. In this situation, drivers can exhibit vigilance decrements which impact their ability to respond to on-road threats. This is of particular concern in situations when the partially automated vehicle fails to respond to a potentially critical situation and leaves all responsibility to safely navigate to the driver. This paper reviews situations that lead to vigilance decrements and characterizes the different methodologies of measuring driver vigilance during PAD, highlighting their advantages and limitations. Based on our reading of the literature, we summarize several factors future research on vigilance decrements in PAD should consider. (shrink)