While the negative effects of alcohol on driving performance are undisputed, it is unclear how driver attention, eye movements and visual information sampling are affected by alcohol consumption. A simulator study with 35 participants was conducted to investigate whether and how a drivers level of attention is related to self-paced non-driving related task (NDRT)-engagement and tactical aspects of undesirable driver behaviour under increasing levels of breath alcohol concentration (BrAC) up to 1.0 %o. Increasing BrAC levels lead to more frequent speeding, short time headways and weaving, and higher NDRT engagement. Instantaneous distraction events become more frequent, with more and longer glances to the NDRT, and a general decline in visual attention to the forward roadway. With alcohol, the compensatory behaviour that is typically seen when drivers engage in NDRTs did not appear. These findings support the theory that alcohol reduces the ability to shift attention between multiple tasks. To conclude, the independent reduction in safety margins in combination with impaired attention and an increased willingness to engage in NDRTs is likely the reason behind increased crash risk when driving under the influence of alcohol.