Although Cortana lacks many features its mainstream competitors had for many years, email integration will no longer be one of them. The company has officially rolled out Outlook integration
for the Halo-inspired virtual assistant on Windows 10, and the Invoke. With this, it will allow you to ask if you received any new emails, and it will then respond with a list of senders and the message sent by them. Beyond that, it offers deeper functionality, that allows you to ask it for emails from a specific person or entity. Adding to this, it will also let you respond to these messages via dictation.
Outlook integration for Cortana rolled out to a limited base for the time being, with those using the U.S. English language setting on Windows 10 getting access to it. Unfortunately, it does not function alongside iOS or Android devices yet. However, with it being Microsoft, this should change in due course.