Despite the fact that the arxiv has made it possible to disseminate papers well before they are sent to a journal, the process of anonymous peer review is still crucial to physics and the rest of science. Anyone who has at least a couple of published papers has appeared on the radar screen of various journals as a potential referee, and pretty soon the requests to review papers come fast and furious. And it's not a matter of rubber-stamping; I've personally refereed about 100 papers, and recommended less than half of them for publication. Of course, individual referees can behave quite differently; editors like referees who will actually read the paper, are willing to reject it if it's bad, and get the reviews back quickly. I used to be good at all three of those, although my record on the last point has deteriorated seriously of late. Every paper sent to a journal like Physical Review (in all of its contemporary manifestations) is sent to a referee as a matter of course. It wasn't always thus. The current issue of Physics Today has a great article about Albert Einstein's run-in with the journal in 1936.
In his salad days, Einstein published in German journals such as Annalen der Physik, but he eventually switched to American journals after he moved to the U.S. He had published a couple of papers in the Physical Review, which were apparently accepted by editor John Tate without being sent to a referee. These included the famous Einstein, Podolsky and Rosen paper on nonlocality in quantum mechanics, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" But in 1936 Einstein and Rosen submitted a paper on the existence of gravitational waves that struck Tate as suspicious, and he decided to send it to the referee. The Physics Today article reveals that the referee was relativist Howard Percy Robertson. Soon after the initial formulation of general relativity, Einstein predicted the existence of gravitational waves by doing the obvious thing -- examining the behavior of small fluctuations in the gravitational field using perturbation theory. But Einstein and Rosen had attempted to solve the full equations without any approximations, and were able to prove that there were no non-singular solutions; they therefore claimed that gravitational waves didn't exist! Robertson figured out that they had made a classic error in GR -- essentially, they had used a bad coordinate system. He wrote a ten-page report explaining why the conclusions of the paper were incorrect. Einstein explained that he had submitted his paper for publication, not for refereeing.
Dear Sir, We (Mr. Rosen and I) had sent you our manuscript for publication and had not authorized you to show it to specialists before it is printed. I see no reason to address theâ€"in any case erroneousâ€"comments of your anonymous expert. On the basis of this incident I prefer to publish the paper elsewhere. Respectfully, P.S. Mr. Rosen, who has left for the Soviet Union, has authorized me to represent him in this matter.
After this incident, Einstein vowed never again to publish in Physical Review -- and he didn't. The Einstein-Rosen paper eventually appeared in the Journal of the Franklin Institute, but its conclusions were dramatically altered -- the authors chose new coordinates, and showed that they had actually discovered a solution for cylindrical gravitational waves, now known as the "Einstein-Rosen metric." It's a little unclear how exactly Einstein changed his mind -- whether it was of his own accord, through the influence of the referee's report, or by talking to Robertson personally. But it's pretty clear that he would have loved the innovation of arxiv.org.