A very common need these days is to do an email message trace. This can be done the old way in the Exchange Online Admin center or the new way via Mail Flow in the Security and Compliance center.
You simply enter the details and then run a search.
and the output looks like the above, where you can also drill in and get more detail.
As with all things Office 365, you can achieve the exact same thing using PowerShell as I have shown above. The code to achieve this is quite straight forward but I have uploaded it to my GitHub repo to save you the trouble:
Where PowerShell comes into its own is when you need to a variety of tasks, perhaps an investigation of a breach. Using PowerShell you can easily dump all the information to CSV for further analysis rather than having to root it out in the web interface.