Peer review has been used to judge the quality of science for several centuries. It is now the standard method by which proposed research projects are selected and funded by government agencies in much of the world. By focusing on the peer review process that is employed by various agencies in the United States and elsewhere, the advantages as well as the disadvantages of the system are highlighted. Ideally, peer review helps scientists do their jobs better by giving them feedback from others. It also helps control the quality of scientific research and scientific publications. The process makes it more likely that research funding is distributed on the basis of scientific merit and that quality criteria will prevail over social, economic and political considerations. However, the process is often overly bureaucratic, time-consuming and inaccurate. It tends to cater to scientific elitism and to discount more practical considerations. Applicants whose proposals are reviewed frequently get discouraged by unconstructive and negative comments. Reviewers are often frustrated by the sheer volume of paperwork they are asked to review along with the inclusion of detail that obscures more critical issues. Overemphasis on peer review may also discourage the funding of innovative research because peers tend to view research somewhat conservatively. For peer review to be effective, the system must be more efficient in focusing the attention of peers on legitimate scientific issues rather than on considerations that are more effectively handled by agency administrators. Regardless of its shortcomings, however, peer review will remain the mainstay of formal scientific evaluation for the foreseeable future. With the advancement of the Internet and electronic publishing there is the potential, on the one hand, for improving the current system and, on the other, for un-reviewed, second-rate science to further dilute the world's scientific literature. Even in this world of instantaneous communications, some system of quality assurance must survive for science to continue to advance.