Driver inattention is among major contributing factors to traffic accidents. There have been and continue to be efforts by governing bodies, car manufacturers, and researchers to prevent driver inattention or, failing that, to mitigate its effects. Many vehicles nowadays come equipped with driver monitoring systems that can alert the driver to, or compensate for, inattention. Moreover, the research community continues to explore and investigate more robust approaches to deal with inattention. Meanwhile, vehicle automation, to various degrees, is becoming more prevalent, with the human's role in the driving task changing depending on the level of autonomy. This necessitates that inattention detection, moving forward, be studied and designed in view of automation and in the context of a specific level of vehicle autonomy. Driver inattention and vehicle automation interact in a complex way, and that needs to be taken into account in the design of future vehicles. We explore this interaction in this paper in light of research findings, and survey inattention detection systems and attempt to contextualize them within popular frameworks for next-generation autonomous vehicles.