The recent debate on trends in inequality in industrial countries has been marred by the lack of consensus about the relevant concept of inequality. Labour economists are concerned with inequality in earnings, macroeconomists with movements in the wage share, while policy-makers tend to focus on household income inequality. We provide a unifying framework to study the relationship between these three concepts of inequality and the way in which labour market institutions affect them. Institutions emerge as a key determinant of inequality, yet they play different roles depending on the extent to which they complement or substitute each other. As a result, we are able to propose a set of inequality minimizing institutions. Institutions that decrease inequality are, however, associated with higher unemployment, and our analysis allows us to quantify the magnitude of this trade-off.