Racial inequalities in higher education are widely recognised, from the scarcity of black and minority ethnic (BME) professors and vice chancellors, to student attainment gaps and campaigns to decolonise the curriculum. This collection of essays brings together experts' ideas for reducing racial inequality across the sector. It includes perspectives and recommendations from academia, university leadership, diversity practitioners, charities, student unions, and academic disciplines. The ideas range from the most fundamental -- How do we talk about race? -- to the big questions of policy and spending public money. Together this collection offers a set of ideas to help tackle one of society's most persistent problems. Following the Foreword by Baroness Amos and the Introduction by Hugo Dale-Rivas, this Higher Education Policy Institute (HEPI) Report contains the following essays: (1) Race matters: Addressing competing inequalities in higher education (Kalwant Bhopal); (2) Talking about Race in Higher Education (Shân Wareing); (3) Putting the burden of closing attainment gaps off BME staff and students (Amatey Doku); (4) Decolonising History? Reflections on the Royal Historical Society's 2018 Report (Margot Finn); (5) Practitioner Reflections: Making diversity work a success in your institution (Sanchia Alasia); and (6) Achieving change: Lessons for higher education from the Non-Profit sector (Srabani Sen).