School inspection is used by most European education systems as a major instrument for controlling and promoting the quality of schools. Surprisingly, there is little research knowledge about how school inspections drive the improvement of schools and which types of approaches are most effective and cause the least unintended consequences. The study presented in this paper uses interviews with inspection officials and a document analysis to reconstruct the "program theories" (i.e. the assumptions on causal mechanisms, linking school inspections to their intended outcomes of improved teaching and learning) of Inspectorates of Education in six European countries. The results section of the paper starts with a summary of the commonalities and differences of these six national inspection models with respect to standards and thresholds used, to types of feedback and reporting, and to the sanctions, rewards and interventions applied to motivate schools to improve. Next, the intermediate processes through which these inspection models are expected to promote good education (e.g. through actions of stakeholders) are explained. In the concluding section, these assumptions are critically discussed in the light of research knowledge.