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I have been in situations when I submitted a paper to a math journal, but at the end of the refereeing process the final report was not sent to me. It has happened both in case when my paper was rejected or accepted.

Do I have a right to see the report(s) on my paper? Does it depend on a journal?

If it does depend on a journal, I would like to ask specifically on Annals of Math, Journal of Differential Geometry, Advances in Mathematics.

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    $\begingroup$ You can ask nicely, but you don't have a "right" to see the report. And there often isn't much to see. Journals like those solicit quick opinions before they go to the trouble of getting detailed reports, and if those are negative they are often just a few sentences. $\endgroup$ – Andy Putman May 16 '17 at 4:31
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    $\begingroup$ After a 1 year review and a rejection with no reports, I tried to politely ask for a referee report (which must surely exist, after such a long time). In response, the editor I was in contact with forwarded me the "report", which was a copy and paste of my paper's abstract (with no opinions or recommendations whatsoever). So, yes, you can try to ask, but even if you manage to get the reports, I am not sure you will like the answer! Top journals are also known to send back to the authors only excerpts of reports (usually keeping negative points and masking positive ones, to motivate rejection). $\endgroup$ – Raziel May 16 '17 at 7:27
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No, you do not have this right. When this first happened to me (more precisely, to my student), I also was outraged and demanded a report. They replied that this is a journal policy: they decide when to send a report to an author and when not to. Gradually I understood that this is a right of a journal, to establish any policy they find appropriate. At the present time many journals even do not send all papers to referees. Many papers are rejected without refereeing. They show the paper to one or several experts for a "quick opinion". If this quick opinion is negative, (or not sufficiently positive) they just reject the paper without having any formal report. Of course this has a simple explanation: some journals, especially those which are considered highly rated, are really overwhelmed with papers, and it is difficult for them to find a referee for each. As a referee, I also receive too many papers some of which I do not want to read. So sometimes I advise the journal to reject just after a brief look, without writing a report. The time each of us can spend on refereeing is limited.

And in general, what is a "right"? It is a principle recognized by an overwhelming majority in some community. Using this definition, I am afraid that nowadays, the authors do not have a right to receive a report on each paper that they submit. 30 years ago I thought that there exists such a right. Probably this changed.

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    $\begingroup$ It is indeed the right of the journal to establish whatever policy the find appropriate, but it is also your right to publicly shame that journal if you disagree with that policy (especially if it was unclear at the start). From what you describe, it does not seem to be the case, but if it is, I think you shouldn't hesitate to name the journal in question so that the community can think twice about sending papers there. $\endgroup$ – Gro-Tsen May 16 '17 at 13:02
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    $\begingroup$ Of course, you can publicly shame, and I do not hesitate to name the journal which rejected the paper of my student without a report: TAMS. But unfortunately this seems to be the general practice nowadays, $\endgroup$ – Alexandre Eremenko May 16 '17 at 13:05
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    $\begingroup$ Attempting to shame top journals isn't exactly a great career strategy. $\endgroup$ – Noah Snyder May 16 '17 at 19:55
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    $\begingroup$ If you have a paper refereed for a year, and receive no feedback other than a rejection, I think it is well within your rights to ask if there was further feedback and why it took so long to get the rejection. If the editor is not forthcoming, you can always bring the episode to the knowledge of the main editor. $\endgroup$ – Pace Nielsen May 16 '17 at 20:17
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    $\begingroup$ @AlexandreEremenko I wasn't using the word "rights" there to speak of legal entitlement. I was using it to mean a morally correct course of action. There is no moral blameworthiness to emailing the editor and asking for more information. Similarly, if the editor handled the rejection poorly (for instance, by holding on to your paper for over a year, and giving you no feedback), it may be proper to explain this to the main editor. That doesn't mean anything will change, but at least you have tried to prevent similar experiences to others. $\endgroup$ – Pace Nielsen May 17 '17 at 15:40
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Since this hasn't been mentioned, I should point out that at many journals, the referee is allowed to indicate whether they are willing for their report to be shared with the author. The editor is then, I feel, obligated to follow the referee's desire.

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To my knowledge, this does not happen with any journal for which I'm an editor. If rejected without a ref, the author is told the editors do not feel it is suitable for our journal, often with a recommendation to try `lower' - said more politely.

Any one having this problem, do let us know the journal.

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Referees are allowed to indicate the comments for authors and editors respectively in separate fields in the review system of many journals.

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The main function of the journal is to assess the quality of the paper and to accept or reject based on that assessment. The decision may or may not be supported by a report, which I understand is optional.

In the current system, with very little if any reward for refereeing, the referee may not feel motivated enough to invest more time into writing an extensive report, unfortunately.

In particular, the rejection decision may be based on a "quick opinion" of an expert, in which case no report is needed. However, in case of rejection, some reason should be named.

In other cases, the journal has hard time finding a referee. Or the referee became unresponsive and the editor has to ask someone else, that can repeat a few times, until the editor gives up and returns the paper, again, without any report. Especially if the paper is difficult to read and understand but the referees do not want to reject simply based on the paper's (un)readability.

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