Immune-checkpoint inhibitors targeting PD-1 or PD-L1 have already substantially improved the outcomes of patients with many types of cancer, although only 20-40% of patients derive benefit from these new therapies. PD-L1, quantified using immunohistochemistry assays, is currently the most widely validated, used and accepted biomarker to guide the selection of patients to receive anti-PD-1 or anti-PD-L1 antibodies. However, many challenges remain in the clinical use of these assays, including the necessity of using different companion diagnostic assays for specific agents, high levels of inter-assay variability in terms of both performance and cut-off points, and a lack of prospective comparisons of how PD-L1+ disease diagnosed using each assay relates to clinical outcomes. In this Review, we describe the current role of PD-L1 immunohistochemistry assays used to inform the selection of patients to receive anti-PD-1 or anti-PD-L1 antibodies, we discuss the various technical and clinical challenges associated with these assays, including regulatory issues, and we provide some perspective on how to optimize PD-L1 as a selection biomarker for the future treatment of patients with solid tumours.