The combination of evidence from independent studies has a curious history. The origins reach back at least to the beginning of the 20th century. Since the mid-1970s, meta-analysis has become popular in several fields, among them medical statistics and the behavioural sciences. The most widely used procedures were perfected in early papers, and subsequently, a kind of groupthink has taken hold of meta-analysis. This explains the need for a review in a statistics journal, destined for a statistical audience. Meta-analysis is not a hot research topic among graduate students in statistics, and by writing this article, we hope to change this. We wish to point out the shortcomings of the mainstream view and exhibit some of the open problems that await the attention of statistical researchers. A host of competent reviews of meta-analysis have been published, and several book-length treatments are also available. We have listed many of these in the bibliography but cannot guarantee completeness.