•We modelled principals self-reported reactions to school inspections.•School inspections drive improvement by setting expectations of good education.•Expectations also narrow instructional strategies and discourage experimentation.•Stakeholders’ interest and sensitivity to inspection reports is another driver.•Self-evaluations and improvement of capacity building and instruction are mediators. Inspection is employed by most European education systems as an instrument for controlling and promoting the quality of schools. Yet there is little research knowledge about how inspection drives the improvement of schools. The study reports on surveys to principals in primary and secondary education in six European countries to attempt to clarify how school inspection impacts on the improvement of schools. Based on an analysis of principals’ perceptions the evidence suggests that inspection primarily drives change indirectly, through encouraging certain developmental processes, rather than through more direct coercive methods. Inspectorates that set clear expectations and standards have an impact on the increased utilization of self-evaluation and on developing the capacity of schools to improve in a variety of ways.