Recent years have seen growing interest in the development of self-driving vehicles that promise (or threaten) to replace human drivers with intelligent software. However, current self-driving cars still require human supervision and prompt takeover of control when necessary. Poor alertness while controlling self-driving cars could hinder the drivers' ability to intervene during unpredictable situations, thus increasing the risk of avoidable accidents. In this paper we examine the key factors that contribute to drivers' poor alertness, and the potential solutions that have been proposed to address them. Based on this examination we make some recommendations for various stakeholders, such as researchers, drivers, industry and policy makers.