More than 95% of the £2 billion of public funding for medical research each year in the UK is allocated by peer review. Long viewed as a respected process of quality assurance for research, grant peer review has lately been criticised by a growing number of people within the scientific community and without. Detractors highlight its perceived inefficiency, and structural flaws that compromise its effectiveness in allocating funding. This report presents the findings of a wide-ranging literature review to evaluate these criticisms. It concludes with a short discussion of simple modifications to the peer review process that might help to address some of them. The research for the report was conducted with funding support from RAND Europe's Health R&D Policy Research Unit with the Department of Health (England). It is available in English only.