Permissions to reproduce an image while writing review papers
Usually the journal you are submitting to, will have instructions (even a form with legalese).  

If it is just for your thesis, I don't think you need to be hyper legalistic, but ask for permission for the intended use (in your thesis).  Email is sufficient (don't need a signature, but don't rely on word of mouth either.  If part of the thesis ends up becoming an article later, just go back at that time and ask for the fuller permission using the journal's advised form or instructions.