Apart from research investigating what works in the field of school inspections, research is also required into what aims inspections should pursue. These 'desirable aims' should be defined by the shared expectations of various stakeholders in the field of education, including inspectors as well as policy-makers and other professionals with a role in quality assurance in education. This chapter reports on a Delphi study within the Flemish education system with 15 stakeholders with the aim of contributing to the construction of an inventory of different aims that inspections should pursue, as well as the implications of these aims on the administration of inspections. The Flemish inspection system is characterized by the very strict distinction between school inspectors (to control schools) and school counsellors (to give advice to schools). Several assumptions underlie this policy, for instance the idea that an Inspectorate that controls schools, is not able to make an independent verification of the school quality when it is also involved in terms of providing advice to the school. The strict distinction is also related to the constitutional principle of 'Freedom of education', which--from an interpretative standpoint--implies that an Inspectorate should merely be focused on school output and results. This study shows that notwithstanding this policy, there is an increasing demand on Flemish school inspectors to contribute to school development and therefore to move beyond accountability-oriented aims. Based on a written questionnaire in the first research phase, three general aims and 62 stated aims were defined for an inspection to pursue. However, the second and third research phased showed that not different stakeholders could not reach a consensus with regard to every single aim proposed by the study. This chapter shows that raising questions on the purpose of school inspection, unearths differing views on fundamental issues and ideologies within the field of education policy and from there to different views on what inspections should look like. [For the complete volume, "School Inspectors: Policy Implementers, Policy Shapers in National Policy Contexts. Accountability and Educational Improvement," see ED613001.]