Recent concern about the effectiveness of alternative treatments in medicine and health, in education, in psychology, and in the social sciences has led to a consideration of how to combine or synthesize the results of independent studies. Historically, integration of independent results focused on how to combine p-values. More recently the emphasis has been on estimating effect sizes, which in turn has motivated a variety of alternative models depending on the experimental conditions. We here review the development of the field with an emphasis of diagnostics and future research.