There are increasing calls within Australia and internationally for schools to be research-engaged, for teaching to be research-rich and for researchers to engage with end-users. Such aspirations raise important questions about whether and how Australian schools are engaging in and with research. This paper reports on an empirical study, Catholic Education Melbourne's "Understanding School Engagement in Research" project, which sought to better understand research engagement amongst 67 Catholic schools in Melbourne. Drawing on the findings of this project, coupled with a subsequent analysis of wider international literature, this paper shows how schools are selective about their research involvement; are discerning about what the research is on and how it is conducted; access research in indirect and informal ways; value research more than they use it; and need much more than research access. The paper concludes by synthesising these five themes into a conceptual framework for understanding and improving school research engagement, and outlining the implications for research organisations, schools and jurisdictions.