What do you do when you are asked to perform an official review for a journal of a manuscript written by your supervisor?

If this is an informal request for internal review -- definitely go ahead. It is common practice to have close associates review work, and your thoughtful comments will gain you respect.

If this is a formal invitation from a journal -- it is a clear conflict of interest. It probably should never have been sent to you, quite honestly. This is not to say you couldn't provide an unbiased, thoughtful review, but to an outsider this would really be questionable. I suggest you take the high road, decline the invitation, and send a letter to the action editor reminding him of your close association.

Definitely don't do it. Write to the editor and decline. Often, journals will have some explicit guidelines on who appropriate referees are and what conflict-of-interest rules apply. Even beyond being able to give an unbiased review is a related standard, which is, "Would this give the appearance of major conflict if this were openly known?" To that end, I would suggest it is always inappropriate to referee papers by:

• Your supervisor (or, the other way around, probably also former trainees)
• Anyone in your department who could be voting on your tenure
• Family members
• Direct competitors (i.e. where there could be a possibility to compete to publish a result first, or where you know you are both applying for the same fellowship).

I think the first three are examples where there is no way to avoid the appearance of conflict of interest. The fourth has a lot more wiggle room, of course, because there can always be some competition if you are close enough to referee the paper well!

The problem is not so much that you couldn't be objective: probably you could. However, it is also for your protection to argue a Conflict of Interest.

Imagine you give a good review, then your judgement will be in doubt, even if justified. The review will not be considered very informative.

Imagine you give a bad one - if that comes out, you can be in a lot of trouble, being in a dependency relation to your superviser.

There are very good reasons to refuse.