We study the effects of robot exposure on worker flows in 16 European countries between 2000-2017. Overall, we find small negative effects on job separations and no effects on job findings. We detect significant cross-country differences and find that labour costs are a major driver: the effects of robot exposure are generally larger in absolute terms in countries with relatively low or average levels of labour costs than in countries with high levels of labour costs. These effects are particularly pronounced for workers in occupations intensive in routine manual or routine cognitive tasks but are insignificant in occupations intensive in non-routine cognitive tasks. A counterfactual analysis suggests that robot adoption increased employment and reduced unemployment, especially in European countries with relatively low or average levels of labour costs, and that these effects were driven mainly by lower job separations.