The concept of intersectionality is reviewed and further developed for more effective use. Six dilemmas in the debates on the concept are disentangled, addressed and resolved: the distinction between structural and political intersectionality; the tension between ‘categories’ and ‘inequalities’; the significance of class; the balance between a fluidity and stability; the varyingly competitive, cooperative, hierarchical and hegemonic relations between inequalities and between projects; and the conundrum of ‘visibility’ in the tension between the ‘mutual shaping’ and the ‘mutual constitution’ of inequalities. The analysis draws on critical realism and on complexity theory in order to find answers to the dilemmas in intersectionality theory.