Q: What does the status on my manuscript submission mean?
I have submitted to a management science journal. The status changed from "Awaiting AE assignment" to "Under Review" in a day. It's been a week since this status change. Does this mean that it is with the AE or has it be sent for peer review?
'Under review' could refer to either review by the desk editor of the journal or peer review by a reviewer. Typically, however, identifying and communicating with peer reviewers does take more than a day, and many journals do subject manuscripts to some internal review based on which appropriate peer reviewers are identified. The timeline here therefore makes it more likely that the manuscript is currently under review by the desk editor. However, as the phrasing of the status is not explicit and subject to some interpretation, it is difficult to say this for certain.
To help you understand submission statuses like this one better, here are a few related resources, including a useful handbook curated by our sister brand, R Upskill.
Hope this helps. All the best for your submission!