We study the effects of robot exposure on worker flows in 16 European countries between 1998-2017. Overall, we find small negative effects on job separations and small positive effects on job findings. Labour costs are shown to be a major driver of cross-country differences: the effects of robot exposure are generally larger in absolute terms in countries with 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. For young and old workers in countries with low levels of labour costs, robot exposure had a beneficial effect on transitions. Our results imply that robot adoption increased employment and reduced unemployment most in the European countries with low or average levels of labour costs.