This is a systematic review conducted of primary research literature published between 2007 and 2018 on the deployment and effectiveness of data analytics in higher education to improve student outcomes. We took a methodological approach to searching databases; appraising and synthesising results against predefined criteria. We reviewed research on the effectiveness of three differentiated forms of data analytics: learning, academic and learner analytics. Student outcomes are defined as retention, academic performance and engagement. Our results find that three quarters of studies report the use of educational data analytics to be effective in improving student outcomes but their relationship with student outcomes requires further and more robust investigation and assessment. We argue that research must interpret and communicate effectiveness qualitatively, as well as quantitatively, by including the student voice in assessments of impact.