Principals are required by policy, regulation, legislation and democratic discourse to promote equity of outcomes. This integrated review investigates research on equity issues facing five student groups: special needs students; religious, cultural and racial minorities; groups disadvantaged by socioeconomic status; gender groups; and students differentiated by their sexual orientations. Sixteen research-based strategies for reducing the gap in achievement between advantaged and disadvantaged students are generated, the strategies being organised within four domains of principal influence: curriculum interpretation, instruction, assessment, and community involvement.