Using New Outlook on Windows for professional communication and productivity
I have what seems to be exactly the same problem: When I send an email, it shows up under "Sent Items", but doesn't reach the recipient. I don't get any message of failed delivery or any other error message. I've even tried sending test emails to myself (the same email address), with the same result - appearance under "Sent Items", but not in the Inbox. It doesn't appear under "Junk" either.
As far as I can tell, I can still receive emails from others just fine.
For me the problem started sometime in the last 24 hours. As far as I know, I have not experienced this problem before. For reference, I'm using outlook.live.com in my browser.