The Microsoft Online Services Team has been posting a series of articles regarding e-mail troubleshooting. The last one is called Troubleshooting Mail Flow Issues in Exchange Online.
“For our latest BPOS Support series video we learn about the tools that administrators can use if issues arise when you or your users are sending and receiving email. Some of the steps in this video include how to check Microsoft Online Services for an outage, checking the MOS Service Health Dashboard, remote connectivity analyzer and checking inbound routing. The support video below should be in every administrators back pocket just in case an issue arises.”