Driving is a routine activity for many, but it is far from simple. Drivers deal with multiple concurrent tasks, such as keeping the vehicle in the lane, observing and anticipating the actions of other road users, reacting to hazards, and dealing with distractions inside and outside the vehicle. Failure to notice and respond to the surrounding objects and events can cause accidents. The ongoing improvements of the road infrastructure and vehicle mechanical design have made driving safer overall. Nevertheless, the problem of driver inattention has remained one of the primary causes of accidents. Therefore, understanding where the drivers look and why they do so can help eliminate sources of distractions and identify unsafe attention patterns. Research on driver attention has implications for many practical applications such as policy-making, improving driver education, enhancing road infrastructure and in-vehicle infotainment systems, as well as designing systems for driver monitoring, driver assistance, and automated driving. This report covers the literature on changes in drivers' visual attention distribution due to factors, internal and external to the driver. Aspects of attention during driving have been explored across multiple disciplines, including psychology, human factors, human-computer interaction, intelligent transportation, and computer vision, each offering different perspectives, goals, and explanations for the observed phenomena. We link cross-disciplinary theoretical and behavioral research on driver's attention to practical solutions. Furthermore, limitations and directions for future research are discussed. This report is based on over 175 behavioral studies, nearly 100 practical papers, 20 datasets, and over 70 surveys published since 2010. A curated list of papers used for this report is available at \url{https://github.com/ykotseruba/attention_and_driving}.