I submitted a research article to a reputable mathematics journal in May 2014. The status of my article is still "under review." I have contacted the editor at least three times regarding the delay but have not gotten a reply to any of my mails. Under such circumstances, what can I do? It's really very troublesome and painful for me to bear this.
Can you contact an Associate Editor or another member of the editorial board? More than 18 months with no communication does seem excessively long and the lack of response from the editor suggests something is wrong. You might also try the secretary in the editor's department and ask her if she can get in touch with him.
If you don't hear back from them either, I would withdraw the paper and submit it somewhere else. Hopefully, there's a way to do that in the online system -- but if not, contacting them one last time with the notification should be sufficient. They can't publish the paper without you signing some forms.