After upgrading from Outlook 2013 to 2016, I found that new e-mails were not being downloaded from IMAP into the inbox. Rather, they were only downloaded into sub folders.
To fix this, click File in the top left, click Account Settings and then click Account Settings again.
Now double click the e-mail account that is affected.
Click More Settings… in the bottom right.
Click the Advanced tab.
In the Root folder path box, type Inbox
Click OK to close the dialog
Wait for it to test your settings and then click Close
It’ll now refresh all your folders and your inbox e-mails will start to download